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4<».
■^^■■■^^^i^^^
A PRACTICAL TREATISE
OM
LOCOMOTIVE ENGINES.
PRACTICAL TREATISE
ON
LOCOMOTIVE ENGINES;
A WOmS IIITBHDBD
TO SHOW THB CON8TBUCTXOM, TBB MODE OP ACTING, AND THB USB OF
TH08B BNOINES FOB CONVBTINO HEAYT LOADS ON BA1LWAT8 ; TO OIYB
TBB MBANS OF A8CBBTAININO, ON AN IN8PBCTI0N OF THB MACHINB,
TBB VBLOCITT WITH WHICH IT WILL DBAW A OIYBN LOAD, AND THB
BFFBCT8 IT WILL PBODUCB UNDBB VABIOUB CIBCUM8TANCB8 ; TO DBTBB-
MINB THB aUANTITT OF FUBL AND WATBB IT WILL BBQUIBB ; TO FIX
THB PBOPOBTION8 IT OUGHT TO HAVB, IN OBDBB TO AN8WBB ANT IN-
TENDED pubfose; etc.
FODHDSS OK
A GRBAT MANY NEW EXPERIMENTS,
MADB ON A LAEOB BCALB, IN A DAILY rEACTICS, ON THB LITBSrOOL AND MAN-
CHEITBB, AND OTHBB KAILWATI, WITH MANY OirVBBBNT BNOINBB, AMD
GOMSIDBBABLB TBAINB OV CABBIA0B8.
TO WHICH II ADDBD,
AN APPENDIX;
BVOWINO THB BXFBN8B OF CONYBYINO OOOD8, BY LOCONOTIVB BNaiNBB,
ON BAILB0AD8.
By the COMTE F. M. Q. DE PAJ^BOUR,
rOmMBBI.Y A BTUDBNT OF THB BCOLB FOLYTBCHNiaVB, LATB OF THB BOYAL
ABTIbLBBY, ON THB 8TAFF IN THB FBBNCB IBBVICB, KNIGHT OF THB
BOYAL OBDBB OF THB LBGION D'HONNBVB, OF THB BOYAL
ACADBMY OF BCIBNCBB OF BBBLIN, BTC.
DUBINO A BE8IDENCB IN ENGLAND FOB SCIENTIFIC PUBP08ES.
INCSBA8E0 BT A GBBAT MANY NEW BZPEBIMBNTS AND BB8EABCHE8.
LONDON; JOHN WEALE.
1840.
/Z02,
LONDON:
W. HU0HB8, kino's HKAD COURTt OOUGH SQUARE.
INTRODUCTION
TO THE FIRST EDITION.
Thebe exists no special work on locomotive engines.
Two writers^ Wood and Tredgold,* have indeed, in Eng-
land, slightly touched upon that matter, but only in a
subordinate manner, in treatises on railways; and, be-
sides, they both wrote at a time when the art was scarcely
beyond its birth. Consequently their ideas, their cal-
culations, and even the experiments they describe, have
hardly any relation to the facts which actually pass before
our eyes, and can be of no use to such as wish to acquire
a knowledge of these engines and their employ on rail-
ways.
Many questions had not even been entered into, others
had been solved in a faulty manner. New researches on
the subject became therefore indispensable. This work
will, in consequence, be found completely different from
^ ' A Practical Treatise on Railroads, and Interior Commimi-
cation in general, by Nicholas Wood.' 1st edition, London,
1825; 2d edition, London, 1832.
' A Practical Treatise on Railroads and Carriages, by Thomas
Tredgold.' London, 1825.
VI INTRODUCTION
any thing that has been published hitherto. No facts will
be quoted, but such as result from actual observation ; no
experiments related, but those made by the author hunself,
on a new plan, and with new aims; finally, no theory
exposed, but such as is derived from those experiments.
If at first sight it appear astonishing that no theory
of locomotive engines should exist, the surprise ceases
on considering that the theory of the steam engine
itself, taken in general, has not yet been explained. It
was natural to suppose, that, respecting a machine at
present in such universal use, and on a subject of such
importance, every thing had been said, and every expla-
nation given long ago. Far from this being the case,
however, not even the mode of action of the steam in
these engines has been elucidated. In the absence of such
indispensable knowledge, all theoretical calculations were
impossible. Suppositions were put in the place of facts.
In consequence, we have seen very able mathematicians
propose, on the motion of the piston in steam engines,
analytical formulee, which would certidnly be exact, if all
things went on in the engine as they suppose ; but which
not being founded on a true basis, fall naturally to the
ground, in presence of facts. From this also results that,
in practice, the proportions of the engines have only been
determined by repeated trials, and that the art of con-
structing them has proceeded hitherto in the dark, and by
imitation.
Locomotive engines being first of all steam engines, we
cannot advance in the researches we undertake, without
solving at the same time the question relating to steam
engines in general. There is even a remarkable point to
1
}
TO THE FIRST EDITION. VU
be observed^ which is, that of all sorts of steam engines,
locomotive ones are those which, in their application, have
to overcome the least complicated resistance, and the most
susceptible of a rigorous appreciation. This circumstance
renders them therefore more proper than any others, for
furnishing an explanation of general fetcts common to all
those machines. The theory once satisfactorily established
in regard to locomotive engines, wiU, of course, apply
equally to all sorts of steam engines, and more especially
to those which, like locomotive ones, work at a high
pressure.
We flatter ourselves, therefore, that our researches, A
although apparently confined to locomotive engines, may
at the same time illustrate the principal points of the
theory of steam engines in general.
However, in order to indicate clearly the design of this
work, and to show in what it differs from those that have
preceded it, we think proper to enter here into some
particulars as to the points on which we have new re-
searches to offer, either theoretical or experimental. It
will be seen that those points embrace nearly the whole
subject.
The pressure of the steam in the boiler had been, till
now, considered as invariable in every engine. It was
calculated once for all, and by approximation, according
to the weight on the valve. A great number of obser-
vations will show, however, how much it varies during the
motion of the engine, and how necessary it is to take that
circumstance into consideration, and to make use of a
more exact mode of determination, lest the calculation
should be entirely founded on an erroneous basis.
i
i
VIU INTRODUCTION
The friction of the waggons was^ until now, valued much
too high. This error naturally rendered every calculation
false, by misleading with regard to the true resistance
overcome by the engines. A great number of experiments
on waggons, alone or united in considerable trains, will
have for their object to show the real value of the friction.
The resistance of locomotive engines was still an un-
solved question. We have endeavoured to determine it
by three different processes, which may serve to verify
each other.
The additionol friction created in the engine by the load
it draws, had never yet been submitted to any investiga-
tion. We shall present numerous experiments on that
subject.
The exact determination of the pressure of the steam in
the cylinder, was necessary to explain the mode of action
of locomotive engines, as well as that of steam engines in
general, and to calculate the work they can perform in
different circumstances. The erroneous ideas admitted in
that respect, were the origin of all the faulty calculations,
which experiment contradicted. We trust that the simple
elucidation of that point wiU in a manner lay open the
whole play of the engine.
The evaporating power of the engines was an element
on which no experiment had yet been made, which was
not even introduced in the calculations, and on which>
however, definitively depends the effect these engines are
able to produce. Experiments made on that subject,
upon a great number of engines, will be found in this
work.
An analytical equation, that might be adapted to solve
TO THB FIRST EDITION. IX
the general problem of locomotive engines, was entirely
wanting; that is to say, an equation by which might be
known i priori, either the effects resulting from the given
proportions of an engine, or, vice versd, the proportions
that ought to be adopted, in order tiiat predetermined
effects in regard to load or speed may be obtained. The
trials hitherto made to come to a solution of this question,
being founded on a false principle, had produced formulas
in evident contradiction with facts. A rule had even been
adopted, according to which the practical power of an
engine was considered as equal to the third part only of
its calculated or theoretical power; whereas, the whole
applied power must evidentiy appear in the effect pro-
duced, and we shall see that it really does appear in it*
This imaginary rule is a sufficient proof of the error of the
calculations that were used, and could only lead to dis-
appointments in practical applications. Engines were
constructed, but the effect that they would produce was
unknown. By the introduction of a new element of cal-
culation, wrongly neglected imtil now, viz. the vaporizing
power of the engines, it will be seen, that that question is
solved in the most simple manner possible. From that
equation, and simply by measures taken on the machine,
the velocity and load of a locomotive epgine may be
immediately found, and vice versa, the proportions which
ought to be given to it, to make it answer any intended
purpose. A great number of experiments, made in a
daily practice, will show the accuracy of the formulae.
This is, at the same time, the theory of all high-pressure
steam engines.
Several secondary dispositions of the mechanism of the
X INTRODUCTION
engines had not yet been studied. It will, however, be
seen that they are apt to deprive the machine, in certain
circumstances, of as much as a fourth part of its power.
The effects of these dispositions, and in particular of that
which is called the lead of the slidCy will be submitted to
calculation, and the results verified by special experiments.
The resistance proper to the curves of the railway
deserved also to fix our attention. We shall endeavour to
fix accurately the form of the wheels, and the disposition
of the rails, by which that resistance may most effectually
be remedied.
The consumption of fuel according to the load had not
been determined in a satisfactory manner, and the rule
proposed was contradicted by the experiment. This
question wUl be established in a different manner, and
the results confirmed by facts.
The researches on those points were made on twelve
different engines, and numerous experiments were imder-
taken on each branch of the subject.
The method constantly followed consists in taking, first,
the primary elements of the question from direct experi-
ment; then making use of those elements to establish a
calculation in conformity with theoretical principles ; and,
lastiy, submitting the results to fresh and special experi-
ments, in order to obtain their verification. For the
furtiier elucidation of the formulee, they are each time care-
fully submitted to particidar applications; and, finally,
to extend the use of the work to persons who may wish
to find the results without calculations, the formul® are
followed by practical Tables, suitable to tiie cases which
occur the most frequentiy in practice.
TO THE FIRST EDITION. XI
It does not enter into the plan we have traced our-
selves^ to give an elaborate description of the engine, nor
the measures of its different parts, except those necessary
for the researches we undertake. Such considerations
would lead us too far, and concern more particularly works
on construction. In like manner, the figures of the Plates
added to our work are only meant as illustrations of the
text. They would be too imperfect for any other object.
The untrodden path in which we have been forced to
enter, may have led us into some error. We by no
means pretend to have produced a perfect work, and we
claim indulgence for the mistakes which may have escaped
us in so new a subject. Our chief aim was to be
useful, while seeking a study congenial to our taste, and
occupying the leisure of an inactive life. Early devoted
to other pursuits, belonging to a flEUDaily for several gene-
rations engaged in the military career, and the son of
a General of Artillery, whose footsteps had naturally
traced our direction, our studies would not have taken
that turn, had we not been struck by the powerful effects
of the moter we are going to describe, and by the im-
portant pait it must necessarily act in modem civilisation.
We thought our work would at least have this result, to
call the public attention to the subject. We shall feel
happy if we have succeeded in some of our researches;
and happy also if others, in correcting our errors, shall
at least elucidate the facts upon which we have called their
attention.
All the experiments related in the work were made by
ourselves, witii all tiie care and attention they required.
Some were made in company with engineers of known
XU INTRODUCTION
talent and ability, as Mr. J. Locke, of the Grand-Junction
Railway, and Mr. King, of the Liverpool Oas Works.
We give them in all their details, with a view that every
one may judge of their accuracy; and we mention the
place and date of each experiment, in order to facilitate
their verification by referring to the books, in which is
re^tered the weight of each of the trains.
In regard to the fecility we had of making these nu-
merous experiments, we must say that, having applied to
the heads of the most important concerns of the sort in
England, we were permitted, without restilction, to pene-
trate into the workshops, to take every measure, to collect
all the documents concerning the expenses, and, lasdy, to
make any experiment that appeared necessary to us.
It is with pleasure we acknowledge in the English
character the liberality we have found in the whole course
of our investigations.
To the friendship of Mr. Hardman Earle, one of the
Directors of the Liverpool and Manchester Railway, we
owe in particular our warmest thanks. His obligingness
never abated. Possessing all the qualities of an enlight-
ened mind, he liked taking a part in researches which
appeared to him conducive to the progress of science;
and he permitted us to use all the engines and waggons of
the railway. The beauty of these engines, their number,
which is not less than thirty, the care with which they are
kept, and the immense trade on that line, which gives the
facility, without interfering with the business of the rail-
way, to select loads for experiments as considerable and
as light as one wishes, make that place the only one,
perhaps, in the world, where experiments on a great scale
TO THE FIRST EDITION. XIU
may be made with the same precision as in general can
only be obtained by a small apparatus. It is for that
reason we preferred that railway to any other at present
in activity, either in f*rance or in England.
The same facilities were also offered us by the Directors
of the Stockton and Darlington Railway. Interesting
documents concerning the repairs and expenses of all
sorts^ incurred by that Company, were obligingly com-
municated to us. We owe that obligation to the liberal
authoris&ation of Mr. J. Pease, M.P., Chairman of the
Company, and to the unremitting attentions of Mr. Robert
B. Dockray.
We have studied the subject with all the interest, and,
we might say, with all the enthusiasm it excited in us. In
fact, what a subject for admiration is such a triumph of
human intelligence ! What an imposing sight is a locomo-
tive engine, moving without effort, with a train of 40 or 50
loaded carriages, each weighing more than ten thousand
pounds! What are henceforth the heaviest loads, with
machines able to move such enormous weights ? What are
distances, with moters which daily travel 30 miles in an
hour and a half? The ground disappears, in a manner,
under your eyes; trees, houses, hiUs, are carried away
from you with the rapidity of an arrow; and when you
happen to cross another train travelling with the same
velocity, it seems in one and the same moment to dawn,
to approach, and to touch you; and scarcely have you
seen it with dismay pass before your eyes, when already
it is again become like a speck disappearing at the
horizon.
On the other hand, how encouraging is the evident
/
XIV INTRODUCTION TO THE FIRST EDITION.
prosperity of those fine establishments ! How satisfactory
it is to acquire the proof that the Liverpool and Man-
chester Railway produces 9 per cent, interest, and the
Stockton and Darlington an equal profit! With what
confidence must we not anticipate the future state of such
undertakings, when we know that, besides the above-
mentipned annual interest, the shares of the Liverpool
Railway have risen, in four years,' from £100 to £210;
and those of the Darlington Railway, in eight years, from
£100 to £300 ? What may not society at large expect in
future from this new industry, which will augment, ten-
fold, the capital and produce of the country, by the
immense influence of speedy and economical conveyance !
It is then with the liveliest wish to see this new branch
of industry difiused as it merits, that we have undertaken
the work which we now present to the public.
^ The first edition of this work appeared in French, in the
beginning of 1835.
INTRODUCTION
TO THE SECOND EDITION.
The Introduction to the first edition, which is here
reprinted such as it was published in 18B5, exposes the
plan we had proposed to ourselves in this work, and the
facilities that were afforded us for studying the subject.
But as a first essay necessarily falls short of what is to be
desired, we have since devoted ourselves to new re-
searches, to endeavour, as fieur as in us lies, to supply the
deficiencies which at first we could only indicate.
This task we began in the month of August, 1836, as
will be seen by the dates of the experiments which will be
presented in the work. Unable, at the period of our first
edition, to find a satisfactory means of separating, in our
experiments, the resistance of the air against the trains,
from the friction proper to the waggons, we were con-
strained to take account of that resistance at an average
velocity of 12 to 15 miles per hour, leaving it imited to
the friction of the waggons, tiiat is to say, giving a valu-
ation of those two resistances together at that velocity.
But recognising the want of a more precise determination
of the special value of each of those two resistances, we
XVI INTRODUCTION
undertook^ in the month of August, 1836, on the Liverpool
and Manchester Railway, a series of experiments on the
subject, and published the results of them, blended with
other matters, in a series of papers printed in the donates
reridus of the sittings of the Academy of Sciences of the
French Institut of 1837. And indeed we were not a
little surprised to find in 1839, in the proceedings of the
British Association for the Promotion of Science, a long
article by an English Professor, who, without noticing
these ulterior researches, indulged himself with the satis-
faction of pointing out to us an omission already published
by ourselves, and remedied long since ; and who, in fine,
proposed a new valuation of the resistance of the trains,
according to which, far from separating the resistance
of the air from the friction of the waggons, he pretended
on the contrary that tiie separation was impossible in the
present state of science on the subject.
The experiments which we undertook at the same
period on the Liverpool and Manchester Railway, com-
prise also several other researches, such as the pressure
against the piston caused by the action of the blast-pipe,
the vaporization of boilers in different circumstances of
rest and of motion, the effects of a different proportion
between the fire-box and the tubes, on the total vapor-
ization of the engine, and on its consumption of fuel, &c.
The results of the greater part of tiiese experiments have
been communicated separately to the Academy of Sciences,
in tiie course of the years 1838, 1839, and 1840, and
printed in the Comptes rendus ; but they are now collected
in this edition^ and so arranged, as to complete as much as
possible the data already offered on locomotive engines.
TO THB SECOND BDITION. JCVU
We could have wished all these researdies to be quite
copclusive; but we do not dissemble that many among
them are as yet but very incomplete^ that they require
further study and more varied observations. Such^ how-
ever, as they are, we yet think them capable of leading
to useful results; and, at all events, they will have the
advantage of pointing out the road to. other experimenters
on the same subjects. We shall be among the first to
receive with eagerness the new lights which their labours
may elicit.
The publication of another work, the subject of which
appeared to us to be very important, the Theory of the
Steam Enffine, prevented us, till now, firom bringing out the
•
second edition of the TVeatiee an Locomotive Enginee^
though the first had long been out of print. The adoption,
by a great number of authors and engineers,^ at the theory
and experimental determinations contained in At first
edition, and the re-production of the work in England, in
America, and in Germany, seem to us an ample reward
for all the application and- labour it has cost us. But as
some authors, in rendering an account of our researches,
' In France, M. Navier, member of the Jnstitut; in England,
Professor Whewell, of the Royal Sooietj of London, in the fifth
edition of his Dreatite on Meckatda; in Prussia, M. Crelle, of the
Boyal Sodety of Sciences of Berlin, &c., have adopted these re-
searches ; and in the third edition of his work on Railways, London,
1838, Mr. Nicholas Wood has inserted, in detail, not only all the
ezperpiental determinations of the Treatise on Locomotive Engines,
but even the theory of that engine developed in the same work,
acknowledging, in a slip expressly added at the head of that
I, the source from which he took <that theory.
b
XVm INTRODUCTION
have given a mistaken analysis of them^ or have drawn
from them consequences which we cannot admit, we
deem it necessary to enter into some details on this
subject.
In the edition published in 1838, by Mr. Woolhouse,
of Tredgold^s work on the Steam Engine, page 186 of the
Appendix, the editor, wishing to give a succinct analysis of
our Theory of the Steam Engitie, the same as will be
found developed in Chapter XII. of this work, but spe-
cially applied to locomotive engines, says that our theory
'' may be briefly explained thus : if the evaporating power
of the boiler be capable of supplying a greater quantity of
steam, at the required pressure, than is consumed at the
successive strokes of the piston, it is evident that the
pressure of the steam in the boiler will gradually increase,
provided no portion is supposed to escape through the
safety-valve or otherwise. This increasing pressure will
gradually accelerate the velocity; and finally, when the
engine attains her permanent speed, the quantity of steam
consumed in the cylinder and suj^lied through the steam-
pipe, must evidently correspond with the quantity eva-
porated by the boiler. Thus the author pretends to
introduce a new element into the calculation^ viz., the
evaporating power of the boiler, which again is to be
estimated by the quantity of fire surface ; and, the density
of steam at a given temperature being, according to the
law of Boyle and Mariotte, proportional to the pressure
and inversely as the volume, as in the case of gases, the
evaporating power is measured by the volume of steam,
generated in a given time, multiplied into its pressure.
Such a mode of proceeding,'^ continues Mr. Woolhouse,
TO THB 8ECOXD EDITION. XIX
'^' does not involve any new doctrine or any principle that
had not been laid down by Tredgold in the first edition of
his work.''
If oar theory were really represented by this analysis,
we might perhaps agree that it would offer but little differ-
ence to that of Tredgold; but on recurring to Chapter
XII. of this edition, and more especially to our work On
the Theory of the Steam Engine^ in which the differences
between the old theory and our own are pointed out in
detail, and for the divers kinds of steam engines, it will
be at once recognised that this pretended explanation
cannot give the slightest idea of our theory ; that a most
important principle in it consists in the determination of
the pressure of the steam in the cylinder and its intro-
duction in the equations, a point which is not even alluded
to in the foregoing explanation ; that the old theory, by
coefficients or such as is used by Tredgold, can lead only
to errors; that it gives the load of the engine inde-
pendentiy of the velocity of the piston, supporting there-
fore that tiie engine will always move the same load at
any velocity ; that it gives the vaporization for a known
load and velocity, independentiy of the load, so that a
greater load would not require a greater vaporization;
that it affords no means of calculating the velocity of an
engine with a given load ; while our own gives, without
the least difficulty, the means of calculating the velocity,
and also the load and vaporization, in accordance with
the facts and principles ; that in applying the two theories
to the same engine, the results are so widely different
that, in some cases, the old theory gives twice or three
times the result of our own, as will be seen in the work
XX INTRODUCTIOX
alluded to ; that our theory explains completely the effects
of the atmospheric engine, which could not be calculated,
and those of the Cornish engines, which were so un-
accountable in the old theory, that the effects related to
have been produced by those engines, were reckoned
completely false by many engineers in Great Britain;
finally, that our theory gives the means of ascertaining
the velocity, load, expansion and counterweight, which
produce the maximmn useful effect in a given engine, a
research which ^m^ totally impossible and even inadmis-
sible in the old theory. AU these differences have
escaped Mr. Woolhouse, but they seem to have been
noticed by the engineers of the Corps Royal des Fonts et
Chauss^s, in France, who, in 1839, voted a gold medal
to the theory objected to by Mr. Woolhouse. We there-
fore refer this author to a more attentive perusal of the
work which he criticises.
There has also i^peared in the AtheneBum^ on the
sitbject of the TTieary qf the Steam Engine^ an anony-
mous paper, on which we cannot help saying a word.
The author of this paper, who, whatever he may say to
the contrary, possesses but a very superficial knowledge of
these matters, afiirms it to be heedless to undertake new
inquiries on the steam engine, since he knows all that
is to be known on the subject. He even deems it
^* absurd ^^ to attempt to ground the calculation of the
eflect of steam en^es on the production of steam in their
boiler ! A writer whose ideas on this subject are so clear
and so profound, has indeed a right to cut questions
short, and set himself up as defender of British en-
gineers, whom he declares to be attacked in their honour.
TO THfl 8BCOKD BDITION. XZl
by the very £act of new inquiries on the subject of the
steam engine. With such feelings as these^ the most
foreign to tnie science^ the article is written. As beyond
this, however, the author enters into no scientific discus*
sion, and as, too diffident to take on himself the respon-
sibility of his own judgments, he rests modestly under
the shelter of his incognito, and has even carried the
anonymous system so fieur as to make in public, to the
author whom he has attacked in secret, demonstrations of
esteem, the motives of which all may appreciate at their
real value, we think ourselves excused from stopping to
answer him any further.
Finally, Mr. Josiah Parkes has just published, in the
Transactions of the Insiitution of CwU Engineers of Lon-
don, voL iii., a long paper in which he undertakes the
determination of a coefficient or numerical relation, repre-
senting in mass all the divers resistances which locomotive
engines have tm overcome in their motion, so as to render
useless all separate research, relative to the value of fric-
tion, resistance of the air, &c. With this view he enters
into a long discussion on the experiments of the Treatise
on Locomotive Engines, and on all the experiments on the
same subject published by divers en^eers; and to de-
monstrate the difficulties insurmountable, in his opinion,
and the uncertainty, attending researches of this kind, he
indicates divers verifications which, as he says, these
experiments ought to satisfy. As the author gives on the
subject a great number of arithmetical calculations, the
errors of whidi might not be perceived at a first glance,
we shall here enter, with some detail, into the examination
of his pretended verifications.
\
XXU INTRODUCTION
On seeing thejundamental errors on which his reasoning
and his calculations are grounded, the inaccuracy of the
results at which he has arrived will at once be recognised.
1st. Mr. Parkes proposes to calculate the pressure at
which the steam was necessarily expended in the cylinder
of each engine submitted to experiment, in order after-
wards to compare that pressure with the pressure resulting
from the totality of the divers determinations of resistances
exerted against the piston, according to the Treatise on
Locomotive Engines. With this view, he seeks, from the
velocity of the engine, the number of cylinders-full of
steam which were expended per minute. Comparing the
volume thus obtained to the volume of water vaporized in
the boiler, he concludes the relative volume of the steam
during its passage into the cylinder ; and finally, recurring
to the Table of the relative volumes of steam under diveiis
pressures, contained in the Theory of the Steam Engine^ he
concludes the pressure which the steam must necessarily
have had. This is conformable to the theory developed
in the Treatise on Locomotive Engines, which, in fact, Mr.
Parkes entirely adopts. But to perform this calculation,
Mr. Parkes takes the average velocity of the whole trip
from Liverpool to Manchester, and from that velocity he
pretends to deduce the mean pressure in the cylinder
during the same trip. Now it will be easy to prove by
an example that this mode is altogether faulty.
Suppose, in effect, the engine Atlas have travelled a
distance of 30 mUes in an hour and a half, vaporizing 60
cubic feet of water per hour. As the wheel of the engine
is 5 feet in diameter, or 15*71 feet in circumference, as
there are two double cylinders-full of steam expended at
TO THE SECOND EDITION. XZlll
every turn of the wheel, and as the capacity of those two
double cylinders, including the filling-up of the steam-ways,
amounts to 4*398 cubic feet, it follows that the volume of
the steam which passes into the cylinders per mile per-
formed, or per distance of 5280 feet, is — —- x 4*398
^ ' 15-71
= 1478 cubic feet.
This premised, when Mr. Parkes refers to the average
velocity of the whole trip, to value the pressure in the
cylinder, as that velocity was 20 miles per hour, and as
the vaporization at the same time was 60 cubic feet of
water per hour, he finds for the ratio of the volume of
1478 X 20
the steam expended to the volume of water, —
^ 60
=492*7. And consequently, riecurring to the Table of the
relative volumes of steam under different pressures, he
obtains for the corresponding total pressure 56*66 lbs.
per square inch ; and, deducting the atmospheric pressure,
he obtains for the effective pressure, 41*95 lbs. per square
inch.
But to show that this mode of calculating, from the
average velocity, can only lead to error, let us suppose that,
by reason of the divers inclinations of the portions of the
railway, the first 15 miles have been traversed in half an
hour, and the other 15 miles in an hour, which still makes
30 miles in an hour and a half; as 30 cubic feet of water will
have been vaporized in the first half hour, or during the pas-
sage of the first 15 miles, and 60 cubic feet of water during
the next hour, or in the passage of the last 15 miles, it is
plain that the volume of the steam will have been respec-
tively in each of those times, — ^ — ^ .= 7^9, first, and
30
XXIT INTRODUCTION
afterwards ' ^ = 369*5 . Whence restdts. accord-'
60 '
ing to the Table, that the effective pressure of the steam
will have been successively 21*62 and 62-95 lbs. per square
inch.
Thus^ during the first half hour the effective pressure
will have been 21*62 ; during the second half hour it will
have been 62*95, and during the third again 62*95. Con-
sequently, taking account of the time during which the
pressure has had these respective values, it is plain that
the mean effective pressure in the cylinder will really have
1 _ 21*62 + 62*95 + 62*95 _ .^.i ^^ _ • i,
been ■ ■ =s 49*1/ ms, per square mch,
and not 41*95 lbs. per square inch, as it is given in Mr.
Parkes^s calculation ; which, by the fact, supposes all the
portions of the trip to have been performed in equal times.
In this case, therefore, which has nothing in it but what
is very ordinary, there would be an error of 7*22 lbs. per
square inch out of 41*95 ; that is, an error of more than -^
on the effective pressure of the steam. It is evident that
the calculation, such as Mr. Parkes makes it, is exact only
for portions of road composed of one inclination or tra-
velled with uniform velocity, and that it cannot apply to
the total passage of a line composed of different incli-
nations. For further elucidations on this head we refer
to Chap. XVII. of this work, relative to inclined planes,
and to Chap. XII., in which all the experiments con-
sidered by Mr. Parkes are calculated.
2nd. We have just shown a first error which Mr. Parkes
introduces, as a fundamental basis, in his calculation of
the pressure of the steam in the cylinder. But he does not
TO THB 8BCOND EDITION. ZXT
»
stop there. In the Table of experiments on the yaporisar
tion of the engines (Chap. V. Art. IV. § 1 of the Treatiie
Oft Locomotive Engines, 1st edition^ and page 258 in this)^
we have given the average velocity of the engines during
each trip ; and that velocity is obtained simply by dividing
the whole distance performed by the time employed in
performing it^ as is seen in the Table in question. It would
be natural then for Mr. Parkes^ who, as has been said
above, is satisfied with average velocities in his calcula-
tions, to take those which are given in the Table ; but in*
stead of that, he augments almost aU the velocities about i^
Thus, for instance, the Vulcan, which travelled 29*5
miles in 1 hour 17 minutes, and whose average velocity in
consequence appeared to be 22*99 miles per hour, had,
according to him, a velocity of 26*90 miles per hour. The
velocity of the Vbsta rises from 27*23 to 31*60 miles per
hour, and so of the others. The critic falls into this new
error because, in the Treatise on Locomotive Engines,
(Chap. IX. § 2, 1st edition, and p. 311 in this), in
speaking of fuel, it is said that, when the engines ascend
without help the inclined planes of the Liverpool and
Manchester Railway, the surplus of work, thence result-
ing for them, equals, on an average, the conveying of '
their load to -j- more of distance, and Mr. Parkes logically
concludes from this that the velocity of the engine must
be by so much increased. So that if an engine perform
1 mile in 4 minutes, ascending a plane inclined -J^,
which renders nearly five-fold the work of the engine,
it would follow, from this calculation, that the velocity
would not have been 15 miles per hour, but 15 x 5 = 75
utiles per hour, since the quantity of work done would
XXVI INTRODUCTION
have been five-fold ! Mr. Parkes's' error proceeds from
his having applied to the velocity a correction which
belongs only to the work done, and, as a consequence, to
the/iieL
But on examining what effect results from this substi-
tution of the imagined velocity of Mr. Parkes for the
observed velocity, it will be remarked, that whenever an
engine is obliged to ascend without help one of the in-
clined planes of the Liverpool and Manchester Railway, it
exerts in that moment, as we have said, an effort about
five times as great as upon a level, and draws its load less
rapidly. One would deem it then allowable to conclude
that the average pressure of the steam in the cylinder
must be augmented, since, during a certain portion of the
trip, tiie effort is greater, and that the useful effect per unit
of time must be diminished, since during the same time
the useful load is drawn at less velocity. But no. Mr.
Parkes's calculation, by augmenting the apparent velocity
of the engine, demonstrates that, in this case, the average
pressure in the cylinder becomes on the contrary much
less and that the useful effect becomes much greater. So
that the error committed produces itself here in the two
opposite ways.
With these elements Mr. Parkes establishes the whole
of his calculations and of his Tables, to the very end of his
paper; and as, to augment the evil, this pretended correc-
tion happens to be made on one portion of the experi-
ments, without being made on the rest, there results an
inexplicable confusion in all the calculations. Thus also
it happens that his determinations of the horse-power pro-
duced per cubic foot of water vaporized, or of the quan-
TO THE SECOND EDITION. XXVU
tify of water employed to produce the power of one
horse, and all the consequences thence deriyed, are in
every way erroneous.
3rd. After having thus calculated very exactly the pres-
sure of the steam in the cylinder, Mr. Parkes compares
the result which he has obtained, with the total pressure
on the piston resulting from the partial resistances suffered
by the engine, according to the Treatise on Locomotive
Engines; and as, in the first edition of the work, the
author had confined himself to mentioning the pressure
against the piston due to the action of the blast-pipe,
without making any experimental research on the subject,
Mr. Parkes takes the difierence between the two results,
as necessarily expressing the pressure due to the blast-
pipe ; and he demonstrates the inaccuracy of it. Here
we perfectly agree with him; for, besides the errors
already pointed out in his research of the pressure of the
steam in the cylinder, every thing variable that can occur
in the different data of resistance, now passes to the
account of the pressure due to the blast-pipe, and must
necessarily come to falsify the calculation of it. Thus for
instance, in the experiments made with the Firefly, the
boiler lost water by the tubes, and there resulted an appa-
rent vaporissation greater than the true one. A part of the
difference between the calculated and the observed pres-
sure was therefore to be attributed to that cause, though it
could not be accurately measured ; but, by the calculation
of Mr. Parkes, it all passes to the accoimt of the pressure
due to the blast-pipe. Similarly, the resistance of the air,
then imperfectly computed in the total resistance for an
average velocity of about 12 miles per hour, is found, in all
XXYIU INTRODUCTION
cases of greater yelocity, to augment considerably the pres-
sure due to the blast-pipe^ and on the contrary to diminish
it in all cases of less velocity. A contrary or a favourable
wind; waggons well or imperfectly greased, &c*, necessarily
produce similar effects. Thus circumstances, combined
with the errors already introduced into the calculation,
raise or lower that pressure to all imaginable degrees ; and
it will readily be imagined that such a determination can-
not be exact.
4th. Mr. Parkes has observed, in the experiments of
the Treatise an Locomotive Engines, and particularly in
two of them, made on the Lbeds engine, and quoted in
the Theory of the Steam Engine, that the useful effects
produced by the same quantity of water vaporized varies
according to different circumstances ; and he is amaaed at
it; for, as he affirms, the useful effects produced by the
same quantity of water vaporized, in the same time and
under the same pressure in the boiler, ought in all cases
to be identical. But this again is merely an error of the
critic ; for if we suppose a locomotive engine drawii^ a
heavy load at a small velocity, since it is only at a small
velocity that the engine has to overcome its firiction, as well
as the atmospheric pressure against the piston, and, above
all, the resistance of the air against the train, it foUovrs that,
out of the quantity of total work executed, there will be
but a trifling portion lost in overcoming those resistances (
but i^ on the contrary, we suppose the same engine per-
forming precisely the same quantity of total work, but
drawing a light load at a great velocity, it is obvious that
a much greater part of the work done will be absorbed in
moving, at that velocity, the resistance which represents
TO THE SECOND EDITION. XXIX
the friction of the engine, as well as the atmospheric pres-
sure against the piston, and in overcoming the resistance
of the air, which increases as the square of the velocity ;
and consequently there will remain a much smaller por-
tion of it applied to the producing of the useful effect.
Hence, in the two cases considered, the useful effects
produced by the same quantity of water vaporised, so hi
from being identical, will, on the contrary, be very dif-
ferent from each other. Mr. Parkes may, besides, satisfy
himself on this point, by perusing the TTkeory of the Sieam
Bnffine, in which he will find numerous examples of steam
engines, in which the useful effect of 1 cubic foot of
water varies in very wide limits, according to the
velocity of the motion or the load imposed on the
engine. Thus Mr. Parkes's reasoning errs again by
tiie basis itself.
5tli. But there is another prindple to which Mr. Parkes
would subject all the observations of vaporiaation of loco-
motive engines. He remarks that in. the two experiments
above cited, the total resistance opposed to the motion of
the fMston is different in the two cases. Consequentiy,
says he, the quantities of water vaporized by the engine in
the same time must be in proportion to the pressures
observed in the cylinder, and the experim^its must satisfy
this condition.
To establish this new principle, Mr. Parkes recurs to
the Treatise on Locomotive Engines itself. He quotes a
passage in which, supposing the same engine travelling the
same distance with two different loads, the author says posi-
tively that the distance travelled being the same* in both
cases, the number of turns of the wheel, and consequently
XXX INTRODUCTION
the number of strokes of the piston given by the engine^
that is to say^ the number of cylinders-fdll of steam, or,
finally, the total volume of steam expended, mil also be the
same in both cases ; whence results that the same volume
will successively have been filled with two steams at dif-
ferent pressures, or, in other words, at difierent densities ;
and consequently the quantities of water which have
served to form those slibams will be in proportion to
their respective pressures (Chap. IX. § 1, 1st edition).
Thus, this passage establishes very distinctly that the
quantities of water vaporized, /or the same distance, are in
proportion to the pressures of the steam in the cylinder.
But what does Mr. Parkesxx>nclude from this ? Why, that
the quantities of water vaporized in the same time are in
proportion to the pressures in the cylinder. Now, it hap-
pens to be just the contrary ; for if we suppose, by way
of example, the two pressures to be in the ratio of 2 to 1,
the volumes of water vaporized for the same distance will
also be as 2 to 1 ; but if the time employed in performing
the distance in question be two hours in the first case and
one hour in the second, it is plainly the quantities of
water vaporized in two hours and in one hour respectively,
which will be one to the other in the ratio of 2 to 1> so
that the vaporizations per hour, or m the same time, will
be equal instead of being in. the ratio of the pressures.
Thus it is clear again that Mr. Parkes's principle rests but
on a new error, which consists in making a confusion be-
tween the vaporizations for the same distance and the
vaporizations for the same time.
6tii. A final observation of Mr. Parkes is this, that in
some experiments, the locomotive engines produced, for
TO THE SECOND EDITION. XXXI
*
the same quantity of water vaporized^ a greater useful
effect than several stationary high-pressure steam engines^
or even than several condensing steam engines; and
he considers this result as a proof of the uncertainty
of those observations; for, says he, the locomotive en-
gines having to contend with the pressure arising from
the blast-pipe, which the high-pressure engines have
not, and also with the atmospheric pressure, neither of
which resistances the condensing engines have to con-
tend with, it is incontestable that they cannot even pro-
duce equal effects, much less superior ones. But this
reasoning is as unfounded as those we have already
noticed; for since the useful effect of steam engines for
the same vaporization, diminishes as the velocity of their
motion increases, which is found developed, either in the
present work. Chap. XII., or in the Theory of the Steam
Engine^ it is easy to conceive that a locomotive, working,
for instance, at its maximum useful effect, that is to say,
with its maximum load, and consequently at a very
small velocity, at which -the pressure due to the blast-
pipe and the resistance of the air are nearly null, can
produce a useful effect greater, nay much greater than a
stationary high-pressure engine, working on the contrary
with a light load and a great velocity. The same in-
feriority of effect, relative to a locomotive, may also occur
in a condensing engine, because an engine of that system,
working, for instance, at 16 lbs. pressure 'per square inch
in the cylinder, and condensing the steam to 4 lbs. per
square inch under the piston, where the pressure is always
greater than in the condenser, loses, by that fact alone, a
XXXU INTRODUCTIOX
quarter of the power that it applies; whereas a loco-
motive working at 5 atmospheres in the cylinder, and at
a very small velocity, which renders almost null the pres-
sure due to the blast-pipe, suffers, by the opposition of
the atmospheric pressure, a loss equal to but -^ of its total
power. Hence, definitively, in the latter engine, the
counter-pressure against the piston destroys a smaller
portion of the total power applied, and consequently,
without even noticing the difference of the friction of the
two engines, or entering into any other consideration
relative to the velocity, it is conceivable that tiie useful
effect of tiie locomotive may be found the greater.
But if a more complete procrf be desired, it will be
easy to furnish it; for the relative volume of the steam at
16 lbs. per square inch, being 1672 times that of the water,
it is plain that if S represent the number of cubic feet of
water vaporized per minute in the boiler, and if a represent
the area of the cylinder expressed in square feet, 1672 S
will be tiie volume of the steam generated per minute,
16*72 R
whence results that — t will be the velocity assumed
a
by the piston of the engine working at that pressure.
Moreover, the ej^ective pressure of the steam or the load
which the piston can support, i8l6 — 4 = 12 lbs. per square
inch ; which gives 12 x 144 a for the total resistance sup-
ported by the piston. Thus, in the condensing engine,
the effect produced by the number S of cubic feet of water,
is expressed by 1672 x 12 x 144 S = 20064 x 144 S. Cal-
culating in the same manner the case of the locomotive
engine, we find that the effect it produces for the same
TO THE SECOND EDITION. XXXIU
vaporization S, working at the total pressure of 7^ I&s. per
square inch, or at the effective pressure of 60 lbs. per
square inch, is 381 x 60 x 144 S = 22860 x 144 S. There-
fore, finally, its useful effect, per cubic foot of water
vaporized, will exceed that of the condensing engine, and
this again is a circumstance, examples of which will be
found in the Theory of the Steam Engine,
Thus this new peremptory condition which the experi-
ments ought to satisfy is as unfounded as the former ones.
It will be remembered, besides, that the velocities em-
ployed by Mr. Parkes, for locomotive engines, being nearly
all considerably augmented, as has been explained above,
he must necessarily arrive at exaggerated results, for the
effects which he supposes to have been produced by those
engines.
It is remarkable, finally, that in applying the preceding
considerations to aU the experiments published on loco-
motives by different engineers, namely : Messrs. R. Ste-
phenson, N. Wood, E. Wood, and Lardner, Mr. Parkea
finds that the conditions to which he proposes to subject
those experiments are not verified in them. Such a result
ought to have put him on his guard against the validity of
his own arguments: but the want of using equations,
which facilitate so much accuracy in mathematical reason-
ing (and the author accounts for it in telling us that he is
more accustomed to handle the hammer than the pen),
causes him to heap errors on errors, combining and
complicating them unaware, till he arrives at a point
where he does not produce a single result that is not
erroneous.
XXXIV INTRODUCTION
There is matter of surprise in the numberless errors
contained in the paper of Mr. Parkes^ and of which we
have noticed merely the principal ones ; but on inquiring
what was the end he had proposed to himself^ what was to
be the definite consequence of his labour, one is yet much
more surprised. Collecting all the erroneous results which
he has obtained, Mr. Parkes forms a Table in which he
sets in view, on one side, the vaporization effected by the
engine, and on the other side, the useful and the gross
effect produced ; but to the latter he gives the name of
momentum* Then, comparing the vaporization to the
effect produced, and taking an average upon all the ex-
periments which he has collected from all the works pub-
lished on the subject, he presents, as the result of his
labours, the following conclusion, which he proposes to
substitute in place of every other kind of research on
locomotive engines.
When the velocity of a locomotive engine is augmented
^n the proportion of 1*52 to 1, the vaporization necessary
to produce the same effects varies in the following pro-
portions :
To produce the same momentum (the same gross effect,
weight of waggons and engine included), in the proportion
of 1*42 to 1, or in a proportion something less than that
of the velocities; to produce the same commercial gross
effect (the same gross effect including the weight of the
waggons), iu the proportion of 2*43 to 1, or nearly as the
squares of the velocities ; to produce the same useful effect,
in the proportion of 3*11 to 1, or nearly as the cubes of
the velocities.
TO THE SECOND EDITION. XXXV
This is the definitive result which Mr. Parkes has
attained^ and the help of which seems to him to render it
needless henceforward to seek to determine either the
friction of the waggons^ or that of the engines, or the
resistance of the ur, or any thing in fact thift may in-
fluence the effects produced ; researches which itppear to
him to offer insurmountable difficulties. Possessed of the
wholesale result of Mr. Parkes, nothing more will be
needed. Does any one wish, for instance, to know what
load a given engine will draw at 25 miles per hour on a
given inclination ? to know what velocity it will assume
with a load of 60 tons ? to know what is the maximum of
useful effect that it is capable of producing? to know
what proportions must be given to it, in order to ob-
tain desired effects? Why, having recourse to Mr.
Parkes's result, the solution of all these questions is
self-evident !
It is evident, on the contrary, that Mr. Parkes's rule,
even were it exact instead of being founded on erroneous
calculations, could lead to but one thing, namely, that of
finding the gross or useful effect produced by an engine at
the velocity of 30 miles per hour, when the same effect is
known at the velocity of 20 miles. But, even then,
making use of so rough an approximation, in which all is
thrown in the lump : friction of the waggons, friction of the
engine, resistance of the air, resistance owing to the blast-
pipe, &c., the result could never be depended on. As-
suredly, calculations like these do not tend to the progress
of science ; they would rather lead it back again to its first
rudiments. For this reason we persist in our belief that
the only means of calculating locomotive engines, is to
XXXVl INTRODUCTION TO THB SECOND EDITION.
endeavour to determine^ as exactly as possible, each of the
resistances which oppose their motion, and by taking
account of the value of each of those forces in the calcxila-
tion, we may in every case attain a valuation really
founded m principle, of the effects of every kind that are
to be expected from them.
C ONTENTS
Introduction to tbb First Edition
Introduction to thb Second Edition
TAQM
V
zv
CHAPTER I.
DESCRIPTION OF A LOCOMOTIVB BNGINB.
Article I. Detail and disposition of the parts.
Sect. I. Of the Boiler
Sect. II. Of the action of the Cylinders
Sect, iii^ Of the Cranks and Wheels
Sect. IV. Of the Safety-valves .
Sect. Y. Of the Water-Gange
Sect. VI. Of the Slides
Sect. VII. Of the Eccentric Motion
Sect. VIII. Of the Drivers
Sect. iz. Of the Pumps
Sect. z. Of the Regulator
Sect. zi. Of the joints or rubbing parts
Sect. zii. Of the Fire-grate
Sect. ziii. Of the disposition of the different
parts
1
8
9
12
13
14
16
20
25
26
27
27
28
XXXVIU CONTENTS.
Articlb II. 0/ the principal dimensions of the Engines.
PACK
Sect. I. Of the dimensions of the parts from which
the power of the engine is derived . 33
Sect. II. Dimensions of the fire-hox and boiler of
some of the best locomotive engines
of the Liverpool and Manchester
Railway ..... 35
Sect. III. Of the old locomotive engines . . 38
CHAPTER II.
OP THB LAWS WHICH RKOULATS THI MECHANICAL ACTION OP
THB 8TKAM.
Sect. I. Relation between the temperature and
the pressure of the steam in contact
with the liquid . . . .41
Sect. II. Relation between the relative volumes and
the pressures, at equal temperature, or
between the relative volumes and the
temperatures, at equal pressure, in the
steam separated from the liquid 53
Sect. III. Relation between the relative volumes, the
pressures, and the temperatures, in the
steam in contact or not in contact with
the liquid 56
Table of the temperature and volume of
the steam generated under different
pressures, compared to the volume of
the water that has produced it 60
CONTENTS. XXXIX
PAGE
Sect. IV. Direct relation between the relative vo-
lumes and the pressures, in the steam
in contact with the liquid . 61
Sect. V. Of the constituent heat of the steam in
contact with the liquid ... 65
Sect. VI. Of the conservation of the maximum den-
sity of the steam for its temperature,
during its action in the engine 71
CHAPTER III.
OF THB PRB8SUBK OF THE STB AM, IN LOCOMOTIVB BNGINB8.
Articlb I. Of the safety-valves.
Sect. I. Of the pressure calculated according to the
levers and the spring-balance . 82
Sect. II. Of the corrections to be made to the weight
marked by the spring-balance . 87
Articlb II. Of the instruments specially destined to measure
the pressure.
Sect. I. Of the barometer-gauge, or syphon-
manometer ..... 92
Sect. II. Of the air-gauge .... 102
Sect. HI. Of the thermometer-gauge . . .109
Sect.- IV. Of the spring-gauge, or indicator 111
Sect. V. Comparative Table of the divers modes of
expressing the pressure .113
Xl CONTENTS.
rxcB
CHAPTER IV.
OP THB RR8I8TANCB OF THB AIR.
Sect. I. Of the intensity of that resistance on the
unit of surface . . . 1 14
Sect. II. Of the resistance of the air against the
waggons, isolated or united in trains . 120
Sect. III. Table of the resistance of the^air against
the trains 131
CHAPTER V.
ON THR FRICTION OF THR WAGGONS ON RAILWAYS.
Sect. I. Necessity of new inquiries on this subject 135
Sect. II. Of the friction of waggons determined by
the dynamometer . . .137
Sect. III. Of the friction of carriages, determined by
the circumstances of their spontaneous
descent and stop upq^ two consecutive
inclined planes . .139
Sect. IV. Experiments on the friction of waggons . 153
Sect. V. Of the causes of variation in the friction
of carriages 164
CHAPTER VI.
OF GRAVITY ON INCLINED PLANBS .168
CONTENTS. Xli
PAOB
CHAPTER VII.
OP THB PIIB88UER PRODUCBD ON THB PISTON BT THB ACTION OP
THB BliABT-PIPB.
Sect. I. Of the effects of the blast-pipe . .174
Sect. II. Experiments on the resistance produced
against the piston by the action of the
blast-pipe . . - . . 182
Practical Table of the pressifres against the
piston, due to the action of the blast-
pipe 198
CHAPTER VIII.
OP THB PRICTION OP LOCOMOTIVB BN0INB8.
Articlb I. Of the friction of unloaded locomoHve engines.
Sect. 1. Of the divers elements of the friction of
locomotive engines 200
Sect. II. Of the different modes of determining
the friction of miloaded locomotive
engines 203
Sect. III. Friction of the engines, determined by the
smallest pressure of steam necessary to
keep them in motion 205
Sect. IV. Friction of the engines, detemuned by
the dynamometer .213
Sect. V. Friction of the engines, determined by the
angle of friction .... 214
Sect. VI. Table of the results of the preceding ex-
periments on the friction of unloaded
locomotive engines .217
Sect. VII. Of the friction of the mechanical organs
of the engine, and of its friction as a
carriage 220
I
Xlii CONTENTS.
PA6S
Article II. Of the addUional friction of loaded loco-
motive engines.
Sect. I. Of the mode of determination . 223
Sect. II. Ekperiments on the additional friction of
loaded locomotive engines . 228
Sect. III. New devdopements on the mode of deter-
mination employed . . . 235
CHAPTER IX.
OF THE TOTAL RB8IBTANCE ON THE PISTON, RESULTING
PROM THE DIVERS PARTIAL RESISTANCES PRECEDENTLT
MEASURED ........ 238
CHAPTER X.
OF THE VAPORIZATION OF LOCOMOTIVE ENGINES.
Sect. I. Experiments on the vaporization of loco-
motive engines .... 247
Sect. II. Of the influence of the pressure in the
boiler on the vaporization of the
engine 254
Sect. III. Of the influence of the velocity of the
engine on the vaporization of the
boiler 259
Sect. IV. Of the influence of the orifice of the blast-
pipe on the vaporization of locomotive
engines ..... 263
Sect. V. Of the comparative vaporization of the
fire-box and the tubes, > and of the
definitive vaporization of the engines
per unit of heating surface of their
boiler 266
CONTEXTS. xliii
PAGE
Sect. VI. Of the loss of steam which takes place
by the safety* valves, during the work
of locomotive engines . . 274
Sect. VII. Of the water drawn into the cyhnders
in its liquid state, and of the effective
vaporization of the engines . 282
CHAPTER XI.
OF FUBL.
Sect. I. Experiments on the consumption of fuel
necessary ta produce, in locomotive
engines, a given vaporization . 296
Sect. II. Of the most advantageous proportion .to
establish between the fire-box and the
tubes of the boiler, in locomotive
engines ..... 301
Sect. III. Of the consumption of fuel necessary to
draw a given load a given distance 307
CHAPTER XII.
THBORT OF LOCOMOTIVB BNOINBS.
Articlb I. Of the effects of the engines with an indefinite
. load or velocity.
Sect. I. Of the different problems which present
themselves in the calculation of the
effects of locomotive engines .317
Sect. II. Of the elements to be considered in the
calculation of the engines . .319
Sect. III. Of the pressure of the steam in the
cylinder 325
Xliy CONTENTS.
PAOB
Sect. IV. Of the velocity of the eng^e with a given
load 330
Sect. V. Of the load of the engine for a desired
velocity 344
Sect. VI. Of the different expressions of the useful
effect of the engine . . 350
Article II. Of the nuunmum useful effect of the engine.
Sect. I. Of the velocity of maximum useful effect 362
Sect. II. Of the load corresponding to the maxi-
mum of useful effect . 365
Sect. III. Of the measure of the maximum usefdl
effect of the engine 367
Articlb III. Practictd formula for calculating the effects
of locomotive engines, and examples of
their (plication .... 368
Article IV. Experiments on the velocity and load of the
engines ...... 382
CHAPTER XIII.
OF THS PROPORTIONS OF LOCOMOTIVE ENGINES.
Sect. I. Of the divers problems which occur in
the construction of locomotive engines 395
Sect. II. Of the vaporization, or of the heating
surfeure, necessary to enable a locomo-
tive engine to draw a given load at a
desired velocity . . . •. 397
Sect. III. Of the diameter of the cylinders, neces-
sary that the engine may draw a given
load at a given velocity 400
CONTEXTS. Xlv
PAOB
Sect. IV. Of the length of the stroke of the piston,
requisite for the engine to draw a
given load at a g^ven velocity . . 402
Sect. V. Of the diameter of the wheel, necessary
for the engine to attain a desired
velocity with a given load 403
Sect. VI. Of the vaporization, or of the heating
.sur&ce a locomotive engine onght to
have, in order to acquire a given
velocity, producing at the same time
its maximum of useful effect . 404
Sect. VII. Of the pressure in the hoiler necessary
for the engine to draw a given load,
or acquire a desired velocity, pro-
ducing at the same time its maximum
of useful effect .... 406
Sect. VIII. Of the diameter of the cylinder, or of the
stroke of the piston, or of the diame-
ter of the wheel, necessary that an
engine may assume a desired velocity,
or draw a given load, producing also
its maximum useful effect 408
Sect. IX. Of the combined proportions to be given
to the parts of an engine, to enable it
to fulfil divers simultaneous conditions 411
Sect. X. Of the special influence of each of the
dimensions of the engine on the eflects
produced 417
Sect. XI. Of the comparative effects of locomotive
engines upon the wide-g^uge and nar-
row-gauge railways 423
Sect. XII. Practical formulae, to determine the pro-
portions of locomotive engines, accord-
ing to given conditions . .431
Xlvi CONTENTS.
PAGE
CHAPTER XIV.
OF ADHESION 434
CHAPTER XV.
OF THE RSOULATOR.
Sect. I. Of the effects of the regulator on the
velocity of the engine . . 439
Sect. II. Dimensions of the steam-passages in some
locomotive engines . . 445
CHAPTER XVI.
OF THB LEAD OF THE SLIDE.
Sect. I. Of the nature and effects of the lead of the
slide 447
Sect. II. Of the effects of the lead of the slide on
the velocity of the engine . . 455
Sect. III. Of the effects of the lead of the slide on
the maximum load of which the engine
is capable 460
Sect. IV. Of the manner of regulating the lead
of the slide 466
CHAPTER XVII.
OF INCLINED PLANES.
Sect. I. Of the load on a level » which corresponds
to the load on a given inclined plane,
and vice versd .470
CONTENTS. Xlvii
PAGE
Sect. II. Of the velocity of locomotive engines on
inclined planes . . .476
Sect. III. Of the velocity of descent of trains,
on inclined planes where no use is
made of the force of the engine . 480
Sect. IV. Of the duration of the trip, and of the
average velocity of the engines, on a
svstem of successive inclinations . 486
Sect. V. Of the average load of the engines,
during their passage over a system
of successive planes • . . 490
Sect. vj. Of the quantity of work on a level, which
corresponds to the conveyance of a
given load, over a system of known
inclinations ..... 495
Sect. VII. Of the means of ascending inclined
planes on railways . . . .510
Sect. vni. Of the best line for a railway between
two given points .... 514
CHAPTER XVIII.
OF CUBVBS.
Sect. I. Of the effects of curves on railways . 521
Sect. II. Of curves the resistance of which is
corrected bv the conical inclination
of the wheels of the waggons . 522
Sect. III. Of the superelevation of the outer rail to
be employed in curves whose curvature .
is not corrected by the conical inclina-
tion of the wheels . . . .532
Xlviii CONTENTS.
PAGE
APPENDIX.
EXPENSES OF HAULAGE BT LOCOMOTIVE ENGINES ON
RAILWAYS .... 537
Sect. I. Expense for repairs of locomotive engines 538
Sect. II. Expense of fuel '. .551
Sect. III. Expense of locomotive power . 553
Sect. IV. Expense for maintenance of way . 555
Sect. V. Total expense of haulage 559
Sect. VI. Of the expense of horses employed as
a moving power . .569
Sect. VII. Of the net profits . .571
Receipts and expenditure of the Liverpool
and Manchester Railway, from the
commencement of the undertaking to
30th June, 1834 .573
Page 307.— Read Skct. III.
A PRACTICAL TREATISE
ON
LOCOMOTIVE ENGINES;
CHAPTER I.
DESCRIPTION OF A LOCOMOTIVE ENGINE.
hf
ARTICLE I.
DETAIL AND DISPOSITION OF THE PARTS.
Sect. L Of the Boiler.
The plan adopted in this work will, it is hoped,
render it both clear and methodical.
We shall begin by a succinct description of a
locomotive engine, in order first of all to set before
the eyes of the reader the machine which is the
subject of consideration.
We shall then explain the laws which regulate
the mechanical action of the steam, and describe
the instruments in use to measure its pressure ;
which will make known the agent employed to
produce the motion of the engine.
Our attention will afterwards be directed towards
the resistances which the engine in its motion has
B
I CHAPTER I.
to overcome, so that we shall successively en-
deavour to determine as well the resistance jof the
waggons as that which belongs to the engine itself,
either when it moves alone or when it draws a
load after it.
With these primary data we shall pass to the
general theory of the motion of locomotive engines,
and shall lay down the formulae by which to de-
termine, a priori, either the speed the engine will
assume with a given load, the load it will draw at
a given speed, or the proportions which are to be
adopted in its construction, in order to obtain any
intended effect.
We shall then have to consider several addi-
tional dispositions proper to the engine, which may
exercise more or less influence on the expected
effects ; and we shall also treat of some external
circumstances, the result of which may be of the
same nature.
Lastly, we shall show the engine's consumption
of fuel with given loads, and every other kind of
expenditure to which it gives rise.
These inquiries give the solution of all the most
important questions concerning the application of
locomotive engines to the draught of loads. They
will sometimes be necessarily subdivided into several
branches, and require calculations and theoretical
illustrations, of more Or less extent, though always
plain and easy, and a series of experiments more
or less numerous ; but we shall take care to main-
DESCRIPTION. 3
tain, all through our work, the classification we at
present lay down. We begin then by the descrip-
tion of the engine.
Plate I. represents a six-wheel locomotive engine,
followed by its tender. Plates II. and III. represent
a locomotive with four wheels. The mechanism
of these engines is sufficiently simple for a short
description to make their mode of acting under-
stood; which is the only object here intended.
Moreover, whatever this first cursory view may
leave imperfect will be found illustrated by the
developements which we shall have occasion to give
in the course of the work.
The principal parts of the engine are : the fire-
place and boiler, which constitute the means of
raising the steam ; the slides and cylinders, which
are the means of bringing into action the elastic
force residing in that steam; and the cranks and
wheels, by means of which the motion is transferred
from the piston to the engine itself. After having
described those principal parts, we shall pass to some
others of less importance, and then show the particu-
lar place each of those parts occupy in the engine.
Figure 5 gives a complete idea of the boiler.
It shows the body of the machine, composed of
three distinct compartments. That on the right,
or in front of the engine, and which is surmounted
by the chimney C, is called the smoke-box. It is
separated from the two others by a partition tt.
The two other compartments together form the
4 CHAPTER I.
boiler: the hinder one is called the fire-box, and
the middle one, or cylindrical part, is the boiler
properly so called. Both the latter compartments
are filled with water to a certain height cd, but
part of their internal space is occupied by the fire,
as will be explained.
In the hindmost compartment is placed a square
box c, which contains the fuel, or forms the fire-
place of the engine. Between the sides of that
box and those of the compartment in which it is
contained, a space qq is left, which communicates
freely with the remainder of the boiler, and which
is consequently filled with water. The fire-place
is supported in the corresponding compartment,
and joined to it by strong bolts, having the ad-
vantage of giving soUdity to that part of the boiler
which, not being rounded, ofiers less resistance than
the cyUndrical parts.
The fire-place e, being thus placed in the middle
of one of the compartments of the boiler, would
be surrounded on all sides with water, were it not
for the aperture Z, which forms the door of the fire-
place, and the bottom, nriy of the box, which is occu-
pied by a grate, one of the bars of which is repre-
sented at nn. This grate is more plainly shown
in fig. 6, which represents the same fire-box seen in
front.
Near the door I, and on the engine, is placed
a strong supporting plate of iron, represented in
figs. 1 and 2, by BB. The use of this plate is for
DESCRIPTION. 5
the engine-man to stand upon. Directly behind
the engine comes the tender-carriage for coke and
water, so that it is easy for the fireman to throw
coke on the fire by the door I, and to let water pass
into the boiler, whenever it may be necessary. This
supply of water takes place by means of a forcing-
pump, put in motion by the engine itself, and which
will be spoken of hereafter.
The lower part, ntij of the fire-place is occupied,
as we have said, by a grate, and remains conse-
quently open, admitting the external air required
for the combustion of the fuel. The coke thrown
into the fire-place faUs on the grate and is sup-
ported by it. When the fire is lighted, and the
door is shut, the flame of the fuel remains con-
fined in the fire-place. It would have no egress
if a number of small tubes or flues e'e'^ the dispo-
sition of which is better seen in fig. 6, were not to
lead the flame to the chimney, after passing through
the whole length of the second compartment or
cylindrical part of the boiler.
From this construction it will easily be conceived,
that as the fire is shut up in the fire-box, and
completely surrounded with water, none of its calo-
rific parts are lost. Afterwards, the flame, in its
way to the chimney, divides itself among all the
small flues above mentioned. It thus traverses the
water of the boiler, having a considerable surface
in contact with it, and only escapes after having
communicated to the water as much as possible of
6 CHAPTER I.
the caloric it contained. Once arrived at the ex-
tremity f!' of the tubes^ the flame spreads itself in
the smoke-box, and escapes freely through the
chimney C.
We see thus the heat applied here in two dis-
tinct manners. All the water which surrounds the
fire-place is in contact with the ignited fuel; and
the water which is placed in the middle compart-
ment is in contact with the inflamed gases which
issue from the fire-place. We shall refer again to
this distinction, in treating of the vaporization of
the boilers, and we shall endeavour to ascertain if
the efiects produced in each compartment difier
from each other.
To this form of boiler is to be attributed all the
astonishing power of locomotives at the present day.
It pennits, in fact, exposing a very large extent of
surface to the action of the fire, and consequently
to develope a considerable quantity of steam, using
at the same time a boiler of very small dimensions,
which is necessary for engines which have to carry
their own weight wdth their load. And, moreover,
it must be remarked that all the efiect produced
by the tubes is obtained without burning any more
coal, and in merely employing the caloric, which
would otherwise be lost. As in the action of loco-
motives, all finally depends on the quantity of steam
that can be developed in the boiler in a given time
with the least possible expense, it will readily be
conceived that this invention is unquestionably the
DBSCRIPTION.
most important that has been introduced into the
construction of locomotives since their. origin.
It may be necessary to observe here, that this
form of a boiler, with tubes, is a French invention.
This ingenious idea belongs to M. Seguin, civil
engineer and manufacturer in Annonay.^
^ M. Segain'8 patent bears the date of the 22nd of February,
1828 ; and it was not until April 25, 1829, that the committee of
directors of the liyerpool Railway called the attention of the
English mechanicians towards locomotive engines, by proposing
a prize on the subject. On October 6, of the same year, 1829,
and not before, appeared the Rocket engine of Messrs. Stephenson
and Booth, the principle and even the form of which difier in no
way from M. Segpiin's patent. Without then by any means
detracting from Mr. Booth's merit in having also conceived that
ingenious idea, the prior claim rests, nevertheless, with the
French engineer.
The fact may be easily verified in England, by looking for a
description of the patent in some of the following works, which
are certainly to be found in the British Museum and other chief
Elnglish libraries : Anmales de l' Industrie JFhm^aise et Etranghv,
ou Recueil Industriel et Manufacturier, atmie 1828 ; Bulletin de la
Sociiti d' Encouragement pour V Industrie Nationale, amnie 1828 ;
Descr^tion des Machines et Procid^s cansignds dans les Brevets
d'Invention, de Perfectionnement et d* Importation^ publi^e d'aprks
les Ordres du MuUstre de I'IntMeur et du Commerce. This last
work only gives the description of expired patents ; so that M.
Seguin's will be found in the year 1838.
In an American edition of Wood's work on Railways (page
338) we find, that in 1825 Mr. John Stevens, of Hoboken in the
State of New Jersey, constructed and employed a locomotive
engine, the boiler of which consisted entirely of tubes of very
small diameter filled with water. But as in the boilers we speak
8 CHAPTER I.
Sect. II. Of the Action of the Cylinders.
The second important part of the engine is the
apparatus of slides and cylinders. Fig. 5 is also
designed to show its disposition.
In the upper part of the boiler, that is to say, in
the part occupied by the steam, is a large tube
VW", called the steam-pipe. It is open at one
end V, and leads out of the boiler. By this tube
the steam is conducted into the cylinders. At V,
in the interior of the tube, is a cock or regulator,
the handle T of which extends out of the engine.
By turning that handle more or less, the passage for
the steam may be opened or shut at will.
The steam, being generated in great abundance in
the boiler, and unable to escape out of it, acquires a
considerable degree of elastic force. If at that mo-
ment the cock V^ is opened, the steam, penetrating
into the tube by the aperture V, follows it to the
entrance v of the slide-box. There a sliding valve
X, which moves at the same time with the engine,
opens a communication to the steam successively
with each end of the cylinders, and this steam
drives the piston alternately from one extremity of
the cylinders to the other. The cylinders are
of, it is the flame and not the water that fills the tubes, which
totally changes the principle of their construction, the ftict re-
ported by the American editor does not disprove the remark
established above.
DESCRIPTION. y
placed horizontally at the bottom of the smoke-box,
where the passage of the flame and the sides of that
box protect them against the condensing effect of
the cold air, and keep them in a proper degree
of heat.
The direction of the arrows in the figure marks
the line of circulation followed by the steam, from
its entrance at the aperture V, as far as the slide-
box. In the situation in which the slide is here
represented, passage 1 is open to the steam, and
consequently the piston is pushed in the direction
of the arrow. At the following instant, passage 2
will be open in its turn, and the piston will be
pushed the contrary way. When the steam has
produced its effect, it passes into the tube v\ and is
conveyed by it to the chimney, through which it
escapes into the atmosphere.
The introduction of the steam takes place at V,
in a dome called the steam-dome, purposely ele-
vated, that the jolting of the engine and the ebul-
lition may not cause the water of the boiler to get
into the opening V.
Sbct. hi. Of the Cranks and Wheels.
The piston-rods being set in motion according to
the foregoing explanation, and sliding in guides
which prevent any deviation from a rectilinear
horizontal motion, communicate a rotatory move-
ment to the axle of the two large or drawing
10 CHAPTER I.
wheels of the engine. The transformation of the
alternate motion into a circular one, takes place
after the manner of the conmion foot spinning-
wheel, by means of a crank in the axle. This
effect is clearly represented in fig. 5. There the
steam may be seen forcing alternately the piston
backwards and forwards, and turning the crank yz^
and at the same time the axle and the wheel which
is fixed to it. However, as in the motion of a
crank, there are two points in which the alternate
force that puts it in motion has no greater ten-
dency to move it in one direction than in another,
which takes place when the radius of the crank
happens to be in the direction of the alternate
motion, the two cranks, respectively corresponding
with the two pistons, are placed at right angles to
each other. By that means one of the two has
always its full effect whenever the other ceases to
act, and the power of the engine does not vary.
Tlie two cylinders being placed, as we have already
said, in the lower part of the smoke-box, the piston-
rods communicate directly under the engine with
the two cranks, as appears in the figure. The
crank-axle being set in motion, the wheels, which
form one body with it, turn at the same time, and
the engine is propelled in the same manner as a
carriage which is set agoing by turning the wheels
round by the spokes.
The only fulcrum of the motion being in the
adhesion of the wheels to the rails that support
DESCRIPTION. 11
them, which adhesion causes them to advance in-
stead of slipping round, it might appear doubtfiil
whether, on such an even surface as the rails of a
railroad, the engine could advance by means of the
sole rotatory motion imparted to its wheels, par-
ticularly^hen the engine has to draw a considerable
weight. But experience proves, that however slight
the adhesion of a wheel to a well-polished rail may
appear to be, as, on the other hand, the power
required to draw a load on a railroad is very small,
that adhesion is sufficient, and the engine pro*
gresses, followed by its whole train.
In ordinary cases the adhesion of two wheels is
sufficient; particularly with engines the weight of
which is so distributed that the drawing-wheels bear
a large portion of it. When a great power of ad-
hesion is required all the wheels are made equal.
In that case, if necessary, the wheels of the same
side may be connected together by metallic rods
placed on the outside of the wheels. One of these
connecting-rods is represented in fig. 35, Plate IIL
C is the prolongation of the axle beyond the wheel.
The crank-arm Co is festened to that prolongation
of the axle, and must necessarily turn with it. The
point 0 is a ball and socket joint ; m is a cotton-
wick Sjrphon, by which the oil is fed into the joint ;
nn are keys designed to lengthen or shorten the rod,
which at its opposite end is joined in the same
manner to the crank-arm of the other wheel. The
natural result of this is, that when the wheel or the
'
12 CHAPTER I.
axle C turns, it carries along with it the crank-arm
Co, and thus communicates the same motion to the
other extremity of the connecting-rod, and by it to
the crank-arm of the second axle. Thus the motion
of the machinery is communicated by the two
working wheels to the others, and the engine then
adheres by all its wheels.
In order that, while in motion, the engine may
not sUp off the rails, which, we know, are iron bars
projecting above the ground, the wheels have, on
the inner side, a flange that prevents any lateral
motion. But as, on the other hand, that flange
ought not to be in danger of constantly rubbing
against the side of the rail, the tire of the wheel
is not exactly cylindrical, but slightly conical. Its
diameter is a little larger on the side of the flange
than on the outward side; the consequence of
which is, that, supposing the engine were to be for
a moment pushed to the left, the left wheel, resting
on its broadest part, would pass over more way than
the right wheel, and by that means bring the engine
back to its true place between the rails. Wheels of
such a form may be seen in figs. 3 and 4.
Sect. IV. Of the Safety Valves.
The three preceding points form the foundation
of the play of the engine; the other parts are
merely accessory, that is to say, essential only to
the setting of the former in action. The boiler has
DESCRIPTION. 13
two safety-valves E, F (figs. 1 and 2), one of which,
F, is sometimes shut up in a box^ to put it out of
the reach of the engine-man, and to prevent him
from overcharging it, as he might be tempted to do
in order to obtain from the engine a greater effect,
even at the risk of damaging it. More commonly,
however, this precaution is given up, on account of
its inconvenience.
The object of these valves is to let the steam
escape into the atmosphere, as soon as its elastic
force attains a limit beyond which it might be dan-
gerous to the boiler. They may also, by being
properly loosened, be used to measure the pressure
of the steam ; but as this point demands some de-
velopement, we shall hereafter make it the subject
of a chapter.
Sect. V. Of the Water-Gauge.
A gauge is likewise fixed to the engine to show
at what height the water stands in the boiler. This
gauge is a glass tube, mn (fig. 7), enchased at both
its ends in two verrels aa, with cocks communi-
cating with the interior of the boiler and appearing
outside, as may be seen in the figure. When the
two cocks rr at top and bottom of the tube are
opened, the water penetrates into the tube and takes
the same level as in the boiler. The cock S is
designed to let that water afterwards run off. This
instrument informs the engine-man when the ap-
14 CHAPTER I.
paratus wants a supply from the pump. As, how-
ever, the tubes and other parts of the boiler begin
to suffer, that is to say, are apt to crack, when the
water gets too low in the engine, there are, for still
further surety, on the side of the boiler, two and
sometimes three small cocks, placed at different
heights ; by opening which, one after the other, the
level of the water in the interior may be also as-
certained.
Sect. VI. 0/ the Slides.
Another important object yet remains to be elu-
cidated. We have said above that the slide-valve
admits successively the steam above and below the
piston of each cylinder, the result of which is the
alternate motion, source of the final progressive
motion of the engine. The engine-man then having
opened the regulator or cock that admits the steam
into the pipes, the steam proceeds from the boiler
through the tube v (fig. 8) into the steam-chest or
sUde-box, and, pressing with all its force on the
upper part x of the sliding-valve, compels it to
remain in immediate contact with the plane on
which it slides while performing its motion. When
the slide is in the situation in which it is repre-
sented in fig. 8, the steam takes the way marked 1 ,
acts upon the piston, and pushes it in the direction
of the arrow. In the meanwhile, the steam under
the piston escapes through the passage 2, which
then communicates with the atmosphere by means
DESCRIPTION. 15
of the aperture e. When this first effect has been
produced y the slide, by means of its rod /, is pushed
in the position marked by the dotted lines. Then,
on the contrary, it is the passage 2 which is open to
the steam !Zing from the iSer: it pushes con-
sequently, the piston in the opposite direction to its
first motion, while the passage 1, communicating
in its turn with the aperture e, gives free egress to
the steam that has produced its effect. The al-
ternate motion continues thus: the slide passing
from one position to the other, by which it opens
and shuts successively the passages or steam-ports,
so that the steam may act alternately above and
below the piston. The steam is afterwards led to
the chimney, as will be explained hereafter, there to
augment the current of air by which is caused the
draught of the fire.
The motion of the slide is regulated in such wise
that, in accompanying the motion of the piston, it
nevertheless precedes it by an instant of time ; that
is to say, instead of opening the passage for the
stroke of the piston, just at the moment the piston
is about to begin that stroke, it opens it a httle
beforehand. We shall have occasion to come back
to this point, and it will appear that this disposition,
favourable to the speed of the engine, may be ad-
vantageously employed within certain limits; but
that beyond those limits it is prejudicial to the
maximum load which the engine is able to draw.
16 CHAPTER I.
Sect. VII. Of the Eccentric Motion.
The alternate motion of the slide is performed by
the steam itself. Some attention is requisite to get
a clear conception of this.
An eccentric wheel is fastened to the axle, and
while the axle turns, the eccentric, drawn along by
its motion, pushes and draws alternately the rod of
the slide.
This effect is represented in figures 9 and 10.
The point O is the centre of the axle, the section of
wliich is here hatched. The point m is the centre
of the eccentric, hatched in a contrary direction.
The axle, in turning, draws the eccentric along with
it, and consequently makes the point m describe a
circle round the point O. In that motion the point
m, passing successively to the right and the left of
the centre O, must necessarily push and draw
alternately the shaft L, which acts upon the slides.
On the other hand, the point C representing the
extremity or throw of the crank of the axle, which
is set in motion by the piston, it will appear that
when the steam, pushing the piston from oue end of
the cylinder to the other, makes the crank revolve
half-way round, the axle makes also the half of a
revolution round itself; therefore the point m de-
scribes the half of a circumference round the point
O, and consequently the eccentric pushes the slide-
rod /, from one of its extreme positions to the other,
that is, from one end of its stroke to the other.
DESCRIPTION. 17
Thus placed, by this first operation, the slide now
admits the steam on the opposite side of the piston.
The piston then goes back, makes the axle revolve
again half-way round, whereby the slide is brought
back to its original position, which suits the next
stroke of the piston ; and so on.
The effect of drawing and pushing alternately the
slide-rod, by means of the rotation of the eccentric,
is accomplished by a metallic ring nn fixed to the
end of the shaft L, and in which the eccentric
wheel turns, the surfaces which are in contact being
smooth and lubricated with oil. By this arrange-
ment, while the great radius of the eccentric passes,
in turning, from one side of the centre to the other,
it carries along with it the shaft fastened to the
ring, and communicates to that shaft the alternate
motion.
By this it will be seen that the eccentric wheel
acts here the part of a common crank, for trans-
forming the circular motion of the axle into an
alternate motion applied to the slide, on the con-
trary principle to that which changes the alternate
motion of the piston into a circular motion applied
to the axle of the engine ; but the eccentric dis*
penses with the crank which would have been
necessary in the axle.
However, as by the disposition of the engine the
slide-rod is not in the same plane with the axle, the
eccentric does not communicate the motion directly
to the slide-rod itself, but by means of the cross**
c
18 CHAPTER I.
axle VKl\ whose fixed point is at K; and the
consequence is, that when the eccentric goes back,
the slide-rod advances, and mce versdy as may be
seen in the figure.
A comparison between the figs. 9 and 10, the
difierence of which is a quarter of a revolution, will
make the above-mentioned effects perfectly intel-
ligible.
By examining the motion of the slide (figs. 10
and 26) it will be seen, that while passing from one
of its situations to the other, and when it happens
to be in the middle position, there occurs an instant
during which both the passages or steam-ports are
shut. This efiect takes place at the moment the
slide changes the passages of the steam, and cor-
responds with the point where the piston changes
its direction. This coincidence can only take place
because, setting aside the lead of the slide, the
radius of the eccentric is at right angles with the
radius of the crank. In fact, the slide is necessarily
thus in its middle position, that is to say, changing
the conmnmications of the steam, at the same time
as the piston is at the bottom of the cylinder, ready
also to alter the direction of its motion. This cor-
relativeness of motions is clearly exhibited in the
figure.
The particular advantage of the eccentric being
thus placed at right angles with the crank is, that
the eccentric is in full action when the crank is on
its centre, or the piston at the bottom of the cy-
DESCRIPTION. 19
linder : that is to say, that the slide is in its most
rapid motion just at the moment that it is to open
or shut the steam-ports; which circumstance is
necessary, to prevent time being lost in the al-
ternate effect of the steam.
In order that the steam-ports may not begin to
close immediately after having been opened, the
slide is so disposed, that after having uncovered one
of the ports, it continues its motion for a short space
before beginning to return. This effect, which is
called the travel of the slide, is represented in the
figs. 9 and 11. By this disposition the uncovered
port remains entirely open while the slide is per-
forming its travel going and coming, and the op-
posite port continues to be entirely closed. It will
be remarked that this part of the motion of the
slide is precisely the slowest of its stroke ; but as
the slide begins to pass again over the steam-ports,
it acquires, on the contrary, its greatest velocity,
because the eccentric is then in its most rapid
motion. This disposition then causes the apertures
to be entirely open or closed during the greater part
of the time employed in performmg each stroke,
and to change them as suddenly as possible at the
most favourable moment for so doing.
That the travel of the sUde may not have the
effect of reducing too much the eduction-port e,
care is taken to make the latter of such width that,
notwithstanding the portion of it which is covered
by the flange of the sUde, it still retains a width
20 CHAPTER I.
equal to that of each of the other steam-ports.
Thus, for instance, the width of the steam-ports
is 1 inch each; that of the bars, or separations
between the ports, 1 inch ; and the eduction-port e,
Ijt inch. Then, exclusive of the slight overlap of
the slide, of which we shall presently speak, the
slide may have a travel of ^ inch ; for it is plain
that in the extreme position of the latter, the educ-
tion-port will never be reduced to less than an inch,
which is the width of the steam-ports.
Finally, when the slide is in its mean position,
it not only intercepts at once both the steam-ports,
as is seen represented in figs. 10 and 26, but it
overlaps them by a small flange, the object of which
is to remove all possibility of one of the passages
ever being open before the other is completely
closed. This overlap is usually from ^ to i inch,
and it is plain that, being added to each side of
the slide, it diminishes by so much the travel of
the latter, as has been said above.
Sect. VIII. Of the Drivers.
Until now we have spoken as if there were only
one sUde, but, having said there are two cylinders,
it is clear that there must be a sUde, and conse-
quently an eccentric, to each of them. On the
other hand, the two pistons, alternating one with
the lOther in their motion, that is to say, acting
r
DESCRIPTION. 21
upon two cranks perpendicular to each other, as
has been explained, the radii of the two eccentrics
must necessarily stand also at right angles with
each other. This disposition may be seen in figs. 1 1
and 12, where the piece forming the two eccentrics
is represented in front. To make it more clear it
is marked by hatchings.
This piece must, as has been said, move with
and be carried along by the axle. However, if it
were permanently fixed on the axle, its position
might suit when the engine is going forward, and
not when it is to go backward ; for it will be seen
that, for these two motions, the eccentric must
be fixed in two difierent positions.
This piece is therefore loose upon the axle, like a
pulley on its axis, but it can be fastened to it at
will. To that efiect it has two apertures, repre-
sented at O and O"; and the axle itself carries
two pins tt\ which are called drivers. The
eccentric being placed on the axle between the
two drivers, it is easy to push it, by means of
a lever, either against one or against the other,
until the driver enters into the aperture designed
for it; so that from that moment the eccentric
may be drawn along by the axle. Moreover, if these
two drivers be placed in such a manner that one
may suit the progressive, and the other the retro-
grade, motion of the engine, then, by shifting the
eccentric fix)m the one to the other, the engine may
i
22 CHAPTER I.
be made to go either forward or backward at plea-
sure.
There is no difficulty in fixing the place that the
eccentric must occupy on the axle, either for the
progressive or for the retrograde motion.
Let us suppose, that by pushing the engine
gently along the rails, we bring one of the pis-
tons to be just in the middle of the cylinder, and
that precisely at the same instant, the crank on
which that piston acts is in its vertical position
above the axle, as in fig. 5 ; it is dear that, to make
the engine go forward, the steam must push the
piston forwards, for then the piston will carry along
with it, in the same direction, both the crank and
the wheels. Consequently the slide must admit the
steam by the port No. 1, or be drawn forward as it
is represented in fig. 5, which, by referring to fig. 9,
requires that the radius of the eccentric be hori-
zontal, and placed at the back of the axle. This
is therefore the point at which the driver must fix
the eccentric for the progressive motion.
The engine remaining in the same position,
let us suppose, that we wish, on the contrary, to
dispose it for the retrograde motion. The steam
must arrive on the opposite face of the piston, that
is, the port No. 2 must be opened to it; which
supposes that the slide is pushed backwards, and
consequently that the eccentric is in fix)nt. It is
therefore horizontally, and in front of the axle,
DESCRIPTION. 23
that the eccentric must be fixed by means of the
driver.
This is exactly the position of fig. 12. By ob-
serving the crank A, we see that while that crank
is vertical and above the axle, the driver r, and
the aperture that receives it, are behind, and hidden
by the axle; consequently, the eccentric is hori-
zontal, and in front, — a position which, as we have
seen, suits the retrograde motion. The driver r is
therefore placed for the retrograde motion, since
it keeps the eccentric in that position.
To return to the first case, if we now suppose,
on the contrary, that the eccentric be pushed against
the other driver r , the corresponding aperture of the
eccentric being at (X, that is to say, not being in
firont of the driver, the consequence will be that,
the eccentric not stirring out of its place, the axle
will have to turn half round before the driver can
enter into the aperture. From this it follows, that
if we continue to examine the crank A, it will be
found to have arrived under the axle, while the
eccentric will still be in the front, which is the
poution that suits the progressive motion ; for it is
the same as that of the crank above the axle and
the eccentric behind, which has been explained
above.
Thus, we see that the two drivers / and r, in
figs. 1 1 and 12, being placed at right angles with
each other, and with the cranks of the axle, are
in a proper position, one for the progressive, and
24 CHAPTER I.
the other for the retrograde, motion of the engine ;
and that by pushing the eccentric, by means of a
lever, either on the one or on the other of the
drivers, the effect of the steam on the piston will
immediately be to carry the engine either forwards
or backwards, according to the driver with which
it has been thrown in gear. The lever which causes
the change of position of the eccentric, is placed
in such a manner as to present its handle within the
reach of the engine-man^ on the plate on which
he stands.
Besides these several dispositions, in order that
the man who directs the engine may, himself and of
his own accord, move the sUdes independently of
the motion of the axle, the shafts of the eccentrics
are not invariably fixed to the slide-rods. They are
only fastened to them by a notch U, figs. 13 and
14. By means of a lever acting on the small rod
vfiloy the engine-man can raise the shaft of the
eccentric and disengage it from the notch, as may
be seen in fig. 14. Then the slides are at Uberty to
move independently of the axle ; and therefore it is
easy, by means of two handles represented by PP,
in figs. 2, 3, 4, and connected with the sUde-rods,
to give to the slides the required motion.
In some modem engines, four eccentrics are
employed instead of two ; namely, two for the pro-
gressive motion of the engine, and two for the re-
trograde; either pair being set according to the
direction in which the engine is intended to move.
DESCRIPTION. 25
This arrangement advantageously supplies the place
of the drivers, because it is of a surer effect; but as,
with respect to explication, it amounts precisely to
the same, we shall not here enter into the detail of
that construction.
Sect. IX. Of the Pumps.
Under the body of the engine are two pumps p^
(fig. 2,) the use of which is to replenish the boiler
with water. Each of them is placed immediately
under the piston-rod of each cylinder, and is worked
by it. Each pump sucks the water of the tender
into the cylinder of the pump, on the one hand, and
on the other hand, forces it from the cylinder of the
pump into the boiler, in the usual way. By having
two pumps the replenishing of the boiler is secured,
as, in case one of the two were to get out of order,
the other may easily supply its place. These pumps
are in continual action; yet they can only force
water into the boiler when the cock of the suction-
pipe is opened, thereby to let the water of the
tender come into the cylinder of the pump.
The valve of these pumps is ingeniously made of
a small metallic sphere, resting on a circular seat,
on which it always exactly fits. Its action takes
place by rising within a cylinder, the sides of which
are pierced with four apertures for the passage of
the water. One of these valves is represented in
fig. 15. The water is introduced through er, from
26 CHAPTER I.
the interior of the cylmder> under the spherical ball
which it raises, and is diflPdsed in the body of the
pump by the apertures b b. This form of a valve
never misses its effect; and the pumps which, in
the beginning, were continually out of order, are
free from that defect, since Mr. John Melling, of
Liverpool, first introduced that sort of valve.
Sect. X. Of the Regulator.
The regulator, of which we have spoken above,
and by means of which the passage leading from
the boiler to the cylinders may be more or less
opened, is represented in figs. 32 and 33. It simply
consists of two metallic disks placed above and
exactly fitting each other, both having an aperture
of the same size. The inferior disk is immoveable,
and shuts the pipe through which the steam es-
capes. The superior disk is moveable, by means of
a handle T, which projects out of the engine ; the
stem r of the handle passes through the moveable
disk, and enters the other in its centre, so as to
keep both in a right position over each other. In
fig. 32, these two disks are distinguished from each
other by hatchings running different ways. By
moving the superior disk K, with the handle T,
circularly on the inferior disk, the two apertures
may be brought to correspond exactly with each
other, as in fig. 32, and then the passage is entirely
open. If only partially moved, as represented by
i
DESCRIPTION. 27
the dotted lines in fig. 33, the passage is only
partially opened; and when the two apertures do
not correspond at all, the communication is com-
pletely intercepted : when the passage is thus shut,
it is the steam itself that keeps the two disks in
immediate contact with each other, by pressing
with all its force on the superior disk.
Tins regulator may also be constructed in a dif-
ferent way. It is sometimes made in the form of a
common two-way cock, the steam coining from
above ; but the one described above is most com-
monly used.
Sbct. XL Of the Joints or rubbing parts.
In aU the joints of any importance the oil is fed
without interruption by means of a cup, with a wick-
syphon placed above the joint, as in fig. 35, Plate II.
This cup is made in the form of a school-boy's ink-
horn, so that the velocity of the motion may not
spill the oil ; and there is at the bottom of it a small
tube, penetrating to the entrance of the joint. A
cotton-wick dipping in the oil of the cup passes
into the tube, and, sucking continually the oil out of
the cup, drops it into the joint without interruption.
Sect. XII. Of the Fire-grate.
The grate in the fire-place is not made of a single
piece. It is formed of separate bars, which are
28 CHAPTER I.
placed side by side at the bottom of the fire-place,
where they are' supported at their two ends. The
advantage of this arrangement is the fistcility it
affords of replacing the bars individually by new
ones, when they are worn out by the intensity of the
fire. Besides, if any accident should happen to the
boiler, and make the water run off unexpectedly,
thus endangering the engine, the engine-man may,
by means of a hook, easily turn the bars upside
down, and consequently extinguish the fire immedi-
ately by letting it fall on the road, with the bars
that supported it. It is also thus that every even-
ing the fire-place is emptied, after the engine has
finished its work.
Sect. XIII. Of the disposition of the different parts.
We shall complete this description by showing
on the whole engine, as represented in figs. 1,2, and
3, the places occupied by the different parts of
which we have spoken.
A, Part of the boiler containing the fire-place.
BB, Stand for the engine-man and his assistant.
C, Chinmey of the engine.
D, Place of the cylinders.
E, First safety-valve, with lever and spring balance,
as will be explained hereafter.
F, Second safety-valve, constructed in the same
manner.
G, Glass-tube.
DESCRIPTION. 29
Hy Gauge-cocks.
I, End of the eccentric-rod.
J, Horizontal guides for the head of the piston-
rod, so as to ensure its motion in the exact
direction of the axis of the cylinder.
K, Cross-axle, communicating the motion of the
eccentric-rod to the slide-rod, by means of
the arms KU and K t, which are fixed upon
it. (See figs. 9 and 10.)
h\ Notch for throwing in gear the eccentric-rod
with the cross-axle which works the slide-
rods.
MM, Rod by means of which the engine-man can
raise the eccentric-rod, and throw it out of
gear with the cross-axle which works the
shdes. This is performed by means of the
arms m and m' connected together. When
the engine-man pulls the rod MM, he causes
the arm m' to rise, and with it the small rod
m'o\ which lifts the eccentric-rod out of gear
with the arm KU.
N, Handle, by means of which the engine-man
pulls the rod MM, so as to produce the
aforesaid effect.
PP, Handles to move the slides when they are
thrown out of gear with the eccentrics. The
handles acting upon the cross-axle Q, move
the cross-heads RR, which are fixed to it.
This motion is communicated by means of
30 CHAPTER I.
the rods SS to the cross-heads rr^ which act
upon the axle working the sUdes.
Ty Handle of the regulator, to open more or less
the aperture through which the steam passes
from the boiler to the cylinders.
V, Steam dome, in which the steam is confined
till it can escape through the aperture of
the regulator, and penetrate into the cy-
linders.
U, Man-hole, or aperture closed by a strong iron
plate, and large enough to admit a man into
the boiler, when necessary.
XXX, Iron knees, by which the boiler is fixed to
the fi'ame of the carriage.
ZZy Springs resting at oa on the chairs of the
wheels, by means of two vertical pins pass-
ing through holes in the frame of the engine.
One end of the pin resting on the back of
the spring, and the other on the upper
side of the chair, the whole weight of the
machine is thus supported by the wheels,
but through the intermediate action of the
springs.
bhy Guides for the chair of the wheel to slide up
and down, according as the spring bends
more or less under the weight of the engine.
The upper part of the chair is scooped out
to form a small reservoir for oU. This reser-
voir, as well as those above mentioned, con-
DBSCRIPTION. 31
tains a tube and a syphon-wick, for feeding
constantly the oil upon the axle, at its rub-
bing point with the axle-box.
Cy Suction-tube, by which the feeding-pump draws
the water from the tender, to transmit it to
the boiler. This tube is afterwards continued
by another flexible tube made of hemp cloth,
but supported within by a spiral spring,
and through which the water arrives from
the tender to the pumps of the engine, when
a cock fixed to the tender is opened.
p, Feeding-pump of the engine, which is con-
stantly set in motion by a connexion with
the piston-rod of the corresponding cylinder,
but which cannot force any water into the
boiler, unless the cock which lets the water
come in from the tender be opened.
p\ Handle and rod of the safety-cock of the pump,
serving to ascertain whether the water really
arrives in the cylinder of the pump. This
cock leads without, so that when it is open
and the pump is working, a small jet of
water may be seen issuing from it, which
shows that the pump has its proper effect.
ee. Buffers, or pads stuffed with horse-hair, to
deaden the shocks which may be given or
received by the engine. Their elasticity is
sometimes augmented by means of a spiral
spring within them.
/, Cock, by means of which the water which is
32 CHAPTER I.'
sometimes carried from the boiler to the
cylinder may be let out.
g, Mud-hole, or opening made in the double
casing of the fire-box and closed with a
screw-bolt. In withdrawing this bolt, a
cleaning-rod may be introduced into the
double casing ; and, by means of a forcing-
pump, water may be injected with force,
to cleanse out the clay sediment left by the
boiling of the water. This cleaning is usually
performed once a week.
A, (fig. 3.) Moveable plate or door of the smoke-
box ; by opening which, the ends of the tubes
of the boUer, the cylinders, the slides, and the
steam-pipes leading from the boiler to the
slide-boxes, or froxcL the slide-boxes to the
chimney, are visible. This door is opened
when it is necessary to regulate the slides,
as we shaU see hereafter.
i. Whistle, by means of which the engine-man
announces at a distance the arrival of the
engine. It consists of a sort of inverted
tumbler, against the edge of which, on turn-
ing a cock, the steam is directed. The
forcible rush of this causes a sound nearly
like that of a boatswain's call. This whistle
is also represented fig. 25.
DESCRIPTION. 33
ARTICLE II.
OP THE PRINCIPAL DIMENSIONS OF THE ENGINES.
Sect. I. Of the dimensions of the parts from which
the power of the engine is derived.
The foregoing description applies to the most
modem locomotive engines, such as those we used
for our experiments. But to give a more complete
idea of them, we must say something of their prin-
cipal dimensions.
Locomotive engines may be constructed of all
sizes and proportions, according to the road on
which they are to move and the work to which they
are destined. But to show the dimensions that
have hitherto been most generally employed, we
will give those of the locomotives of the Liverpool
and Manchester Railway, remarking at the same
time, that the engines most frequently constructed
now are those of the largest dimensions, and that
the engines having cylinders of 8 or 10 inches
diameter are only remains of the old engines of the
C!ompany. ' The Liverpool and Manchester Rail*
way is 4 feet 8^ inches wide from rail to rail,
and the velocity does not exceed 30 miles an hour.
For railways of greater width, and whereon a greater
velocity is intended, engines of larger dimensions
have been constructed. The following Table then
is not to be regarded as Umiting the dimensions of
locomotives, but as intended merely to complete the
D
34
CHAPTER I.
foregoing description, by making known the most
usual proportions, and particularly those of the
engines used in the experiments contained in this
work.
Dimensions of the Locomotive Engines on the Liverpool and
Manchester Railway (1836).
Number
Diameter
Diame-
Weight of
Effective pressure
of en-
of the
Stroke of
ter of the
the
in the boiler, in lbs
gines.
cylinder.
the piston.
wheel.
engine.
per square inch.
inches.
inches.
feet.
tons.
lbs.
2
8 to 10
17 and 16
5
7 to 8
50
9
11
16
5
8 to 9
50
6
11
18
5
10 to 12
50
2
11
20
5
11 to 12
50
2
12
16
5
11 to 12
50
2
12
18
5
12 to 12i
50
5
12i
16
5
10 to 11
50
1
14
12
5
Hi
50
2
14
16
5
12
50
2
15
16
5
12i
50
Most of these engines have now six wheels,
two of which, five feet in diameter, are worked
by the steam, and four, three feet in diameter,
are destined merely to sustain the weight of the
engine. Sometimes the six wheels are of equal size,
and are all set in action by the steam, by means
of connecting-rods which conununicate the motion
of the driving-wheels to the four others. The ad-
vantage of this last disposition is to make the engine
adhere to the rails by six wheels instead of two ; but
a very ingenious apparatus, invented by Mr. John
DESCRIPTION. 35
Melling, foreman of the Company's factory at Liver-
pool, and of which we shall speak hereafter in
Chapter XIV., allows the same advantage to be
obtained with wheels of unequal diameter ; which
besides are more favourable to the convenient ar-
rangement of the divers parts of the engine.
The end proposed in adopting six wheels rather
than four is to lessen the wear and tear of the rails
by dividing the weight of the engine among six
supports instead of four. A second motive also is
in view ; namely, to prevent all possibility of acci-
dent in the event of the crank-axle happening to
break. In this case a four-wheel engine would run
the risk of going off the rails, but if supported on
six wheels the remaining four will necessarily keep
it on the line.
Sect. II. Dimensions of the fire-box and boiler of
some of the best engines of the Liverpool and
Manchester Railway.
m
It is from the dimensions we have just noticed,
and more especially from those of the cylinder and
stroke of the piston, that the power of locomotive
engines is generally expressed. It will appear, how-
ever, in the course of this work, that for such
expression of the power to be complete, and really
sufficient to give the effect of the engine under
all circumstances, the evaporating power of the
engine, or, which amounts to the same, the heating
36 CHAPTER I.
surface of the boiler, ought to be considered also.
Without this principal element, an expression of
the power of a steam engine is mere illusion.
In the fire-box and boiler resides, in fact, the real
source of the effects of the engine : the cylinder
and other parts are the means of transmitting and
modifying the power ; but what could be their use,
if that power itself did not exist ?
To complete, therefore, the proportions already
given above, we shall add here a Table of the di-
mensions of the fire-box and boiler in the different
engines to which we shall have occasion to refer.
In another part of the work, our experiments will
enable us to replace this complex datum by the
simple expression of the evaporating power of those
engines. The two most important columns of this
Table are those which show the extent of surface
exposed to^the action of the caloric, whether radi-
ating or communicative.
We introduce the engines in the order of the dates
of their construction. The two engines Goliath and
Fire-fly bear the number 1 , because it will be seen
farther on, in Chapter X., that in rebuilding those
engines, boilers were adapted to them different from
those which they had originally, that is to say, dif-
ferent from those which appear in this Table ; an((
therefore we shall have to distinguish these new
boilers by the number 1 1 .
DESCRIPTION.
37
O
O
I
«5
^^is?
its
fl O V tt s
»^ ^ ** ♦• ^
1^1
SsSS
0000
10 to to to
O
«o
•9
u 01 C9 01 CO CO CO (N ^
0000
to 10 U3 u>
• • • «
00 CO CO 00 01
"S t^ C9 t^ ^ eo
00
• • •
.§0^0
9
t^ CO G4
•* O t^
^_ • • ■ •
00 i-H 00 "-^ w
00
C4 00 o c«
CO <N 00 CO
• • • •
00 00 <^ O
OOdt^Oco i-H ooo)<o;o
00 CO <o r^ t^
9*^ ^ r^ CO CO CO O) t^
\^ t<^ooooco^C9co 01 r^oot^^
^ t^ t>.»r3t^t^C4t^»o CO (NCN»r>^o)
0«t^ OiOCOCOlAO)^ rl* OCOi-iC^
• 00 ^OOC9CIC4^G4 CSI C4CS|C0<N
;0 i-i to t^ CO CO
O 00 Tf 00 CO o
« •
CO O
00 tJ*
^ CT tN, r*. CO
CO CO 00 kO <^
CO <^ t^ ^ r-i
CO CO to o) r^
• • • • •
O) C9 -^ 00 O)
CO CO CO -^ -^
gr<»r<%t^t^CN»r<%r^r<%OC^kOt^t^t^
^^^^<^^^^^coc^OO^Tt*rl*
§
O t^
OiOir^t^t^»oO j^ oor^o<N
t>»COOOO)COOO O) COO<-iO)
Length
of the
boiler
na ^
1
0
0
0
«o
00
0
CO
0
0
00
a|
4^
tea
•
CO
r*
•
CO
CO
•
CO
00
•
t^
•
CO
CO
•
CO
(0
«o
•
00
•
4^
• ^
i
0
10
0
uo
to
00
3 •«
JSS
>o
t^
>o
t^
t^
0
s^
-i
«S
00
Cil
CO
oo
CO
00
CO
Cil
00
(N
oo
00
00
r
S S d
45 ^^ ^wm
^
T*5 I
6
'G)
S
^CO COCOCOCOCOCOCO CO Q0CO00G4
^^^ ^ ^ ^ ^ ^ >,, ^ ^ ^ ^ ^ ^
•• *••••••• «
agg^-g 5-
i
38 CHAPTER I.
It wUl be seen hereafter, that, with a boiler of
those dimensions and of such a form, the engines
are able to evaporate about a cubic foot of water
per minute, or a poimd of water per second, at the
effective pressure in the boiler of 50flbs. on the
square inch.
Sect. III. Of the old Locomotive Engines,
The description given above is applicable to
engines intended for great speed, and particularly
for the conveyance of passengers. That form is
exclusively adopted in all modem railways.
On some lines, however, engines of another con-
struction are to be foimd. The railway from Stock-
ton to DarUngton being used for a different service,
that is to say, for the conveyance of coals and for a
more moderate velocity, it may be proper to give
here an idea of the engines used on that line.
Those engines are of different models, from the
oldest to the most recent ones.
In some the fire passes through the boiler
in a single tube, which serves as a fire-place,
and communicates directly with the chimney. In
some others the tube bends round in the boiler
before it reaches the other end, and comes back
to the chimney, which, in that case, is placed
next to the door of the fire-place. In others, the
tube or flue, when it reaches the end of the boiler,
divides and returns towards the chimney, as two
smaller tubes. . In some, the fire being still placed
DESCRIPTION. 39
in an internal flue, the flame returns to the chimney
by means of about 100 small brass tubes, on a
principle similar to that of the Liverpool engines.
Lastly, three of them are constructed on the same
model as those of Liverpool.
The Company carries both passengers and goods.
The first travel with a speed of twelve miles, and
the second of eight miles, an hour. Of the different
forms of boilers, those only with a set of small tubes
suit for carrying passengers; the others cannot
generate a sufficient quantity of steam for the ve-
locity wanted. But when a speed of eight miles per
hour only is required, the most convenient boilers
have been found to be those with one returning
tube. They generate a sufficient quantity of steam
for the work required of them, and have the ad-
vantage of being cheap in regard to prime cost and
repairs, as their form is simple, and they are entirely
made of iron, whilst the tube boilers require the use
of copper.
Besides the difference in the form of the boilers,
the other parts of the engine differ also. The
cylinders are placed on the outside, and in a ver-
tical position. The motion is not communicated
from the piston to the engine by a crank in the axle,
but by a rod working outside of the wheel, and
resting upon a pin fixed in one of the spokes. Those
engines have in general six equal wheels, of four feet
diameter. Two of the wheels are worked by the
steam, as has been just explained ; and the four
40
CHAPTER I.
others are attached to the former by connecting-
rods, which cause them to act all together.
The weight of these engines varies. Setting aside
those which we have mentioned as being on the
model of the Liverpool ones, and which are very
light, the average weight of the others is from ten
to twelve tons.
All these engines are supported on springs. In
some of the older ones, the water of the boiler,
pressing upon small moveable pistons, and pressed
itself by the steam contained in the boiler, was
intended to supersede the springs; but though
that system displayed a great deal of ingenuity,
the spring it formed was found in practice to be
too variable, and the system was given up.
The usual proportions adopted for the engines on
that railway are the following :
Cylinder
# • ■
14|^ inches.
Stroke
• • 4
. 16 —
Wheels
• ■
4 feet.
Weight
• •
11 tons.
Eifectiye
pressure .
48 lbs. per square inch
The pressure, however, varies according to the
ascertained solidity of the boiler. When the sheets
of which it is formed begin to grow very thin, the
pressure is sometimes reduced to 36fts. only per
square inch; in other circumstances, it is, on the
contrary, increased to J60 fts.
CHAPTER II.
OF THE LAWS WHICH REGULATE THE MECHANI-
CAL ACTION OF THE STEAM.^
Sect. I. Relation between the temperature and the
pressure of the steam in contact with the liquid.
Bbfobb entering upon considerations which have
for their basis the effects of the steam, it may be
necessary to lay down, in a few words, some of the
laws according to which the mechanical action of
the steam is determined or modified.
In the calculation of steam engines it is requisite
to consider four things in the steam.
Its pressure^ which is also called tension or
elastic force, and which is the pressure it exerts
on every unit of the surface of the vessel that con-
tains it.
Its temperature, which is the number of degrees
marked by a thermometer immerged in it.
Its density, which is the weight of a unit of its
volume.
' Thifl chapter has already appeared in the work entitled
" Themy of the Steam Engine" hat we deem it convenient to
give the greater part of it here also, that the reader may not he
ohliged to recur to another work.
42 CHAPTER II.
And its relative volume^ which is the volume of
a given weight of steam compared to the volume of
the same weight of water, or, in other words, to
the volume of the water that has served to produce
it. We deem it necessary to add here the word
relative, in order to avoid the confusion which would
otherwise arise continually between the absolute
volume filled by the steam, which may depend on
the capacity of the vessel that contains it, and the
relative volume which is the inverse of the density.
Thus, for instance, steam generated under the
pressure of the atmosphere may fill a vessel of any
size, but its relative volume will always be 1700
times that of water.
When the volumes occupied by the same weight
of two different steams are compared together, it
is evidently a comparison of what we call the rela-
tive volumes of those two steams. For, the two
steams compared having the same weight, corre-
spond to the same volume of water evaporated.
Therefore it follows that the ratio of the relative
volumes of the two steams is the same as the ratio
of their absolute volumes.
To make this more clear, if S express a given
volume of water, M the absolute volume of the steam
resulting from it under a certain pressure p, and M^
the absolute volume of the steam which results from
it under another pressure p\ the relative volume of
the steam under the pressure p, which relative
volume we will express by /i, will be
OF THE MECHANICAL ACTION OF THE STEAM. 43
M
and the relative volume of the steam uiider the
pressure p , which relative volume we will express
' by /, will be
'^ s
I Consequently will be deduced
/i M
i
A*
' M'^
that is to say, the ratio between the absolute
volumes occupied by like weights of two different
steams, is, as we have said, nothing more than the
ratio between the relative volumes of those steams.
These definitions premised, the steam may be
considered at the moment of its generation in the
boiler, when still in contact with the liquid from
which it emanates, or else as being separated from
that liquid.
When the steam, after having been formed in
a boiler, remains in contact with the generating
water, it is observed that the same temperature
corresponds invariably to the same pressure^ and
vice versd. It is impossible then to increase its
temperature, without its pressure and density in-
creasing spontaneously at the same time ; and it is
impossible also to increase its density or its pressure,
except by increasing at the same time its tempera-
ture. In this state the steam is therefore at its
44 CHAPTER II.
maximum density and pressure for its temperature^
and then a constant connexion visibly exists be-
tween the temperature and the pressure.
If on the contrary the steam be separated from
the water that generated it, and that the tempe-
rature be then augmented, the state of maximum
density will cease, since there will be no more water
to furnish the surplus of steam, or increase of den-
sity, corresponding to the increase of temperature.
That invariable connexion above mentioned, between
the temperature and the pressure, will then no longer
exist, and, by accessory means, the one may at
pleasure be augmented or diminished, without any
necessity of a concomitant variation taking place in
the other, as it happens in the case of the maximum
density.
It is necessary then to distinguish between these
two states of the steam.
One of the most important laws on the properties
of steam is that which serves to determine the
elastic force of the steam in contact with the liquid,
when the temperature under which it is generated
is known ; or, reciprocally, to determine that tem-
perature when the elastic force is known. Not only
is this inquiry of a direct utility, but we shall see
in the sequel that it serves equally to determine the
density or the relative volume of the steam formed
imder a given pressure, a point of knowledge in-
dispensable in the calculation of steam engines.
Experiments on this subject had long been taken
OF THE MECHANICAL ACTION OF THE STEAM. 45
in hand, and they were very numerous for steam
formed under pressures less than that of the atmo-
sphere ; but for high temperatures, the experiments
extended but to pressures of four or five atmo-
spheres. Some few only went as far as eight, and
that without completing the scale in the interval.
The extreme difficulty of researches of this kind, if
it be desired to attain results really exact, the heavy
expenses they occasion, and the danger attending
them, had prevented the experiments from being
carried farther. But to the Academy of Sciences of
the Institute of France we are indebted for a com-
plete Table on this subject. The Academy confided
the conduct of these delicate experiments to two
distinguished scientific men, Messrs. Arago and
Dulong, who evinced in them every nicety that
a perfect knowledge of the laws of natural phi-
losophy could suggest, to avoid the ordinary causes
of error. Never were researches of this kind con-
ducted on so vast a scale, nor with more accuracy.
The pressure of the steam was measured by^ effective
columns of mercury contained in tubes of crystal
glass, which together extended to the height of 87
feet English. The instruments were constructed by
the most skilful makers, and no expense was spared.^
^ Vide Expos^ des recherches faites par ordre de T Acad^ie des
Sciences, poar determiner lea forces ^astiques de la vapeur d'eau
ii de hautes temperatures. Mhunres de TAcadhnie des Scienceg,
tome X. ; Annales de Chimie et de Physique, tome xliii. 1830.
46 CHAPTER II.
Therefore the greatest degree of confidence is to be
attached to their results.
These beautiful experiments furnish a complete
series of observations, from the pressure of 1 atmo-
sphere to that of 24. To form, however, a Table
extending beyond this limit, Messrs. Dulong and
Arago have sought to deduce from their observa-
tions a formula which might represent temperatures
for still higher pressures without any noticeable
error. They have in fact attained that end, by
means of a formula which we shall presently report,
and whose accord with experience is such, for all
that part of the scale above four atmospheres, as to
give room to think that, on being appUed to pres-
suiea up to 50 atmospheres, the error in tempera-
ture would not in any case exceed 1 degree of the
centigrade thermometer, or 1*8 degree of Fahrenheit.
They were enabled then, as well from the result of
their observations as by means of an amply justified
formula, to compose a Table of temperatures of
steam up to 50 atmospheres of pressure, with, the
certainty of committing no error worthy of note.
Though the formula of Messrs. Arago and Dulong
may be applied to pressures comprised between 1
and 4 atmospheres, with an approximation that
would suffice for most of the exigencies in the arts,
they did not indicate the use of it for that interval,
because in that part of the scale other formulas
already known accord more exactly with the results
of observation, and ought, in consequence, to be
OF THE MECHANICAL ACTION OF THE STEAM. 47
preferred. Among those formulse, that originally
proposed by Tredgold, and afterwards modified by
his translator, M. Mellet, gave the most exact
results ; and no inconvenience arises from the use
of it, when it is required merely to compose a Table
by intervals of half-atmospheres. But as, for the
more commodious use of the formulae which we have
to propose in this work, we shall want to establish a
Table by intervals of pounds per square inch ; we
deem it better to employ a formula which we shall
give with the others presently, and which, approach-
ing as near as that of Tredgold to the results of direct
observation, in the points furnished by experiment,
has moreover the advantage of coinciding exactly
at 4 or 4^ atmospheres with the formula of Messrs.
Dulong and Arago, which is to form the continu-
ation of it.^
^ In fact, comparing, in French measure, the two formulae with
the observation, we find the following results, as it will be easy to
verify hereafter!
Elastic force
of the steam
in atmo-
spheres.
Observed
temperature,
by the centi-
grade ther-
mometer.
Temperature
given by Tred-
gold's formula,
modified by
MeUet.
Temperature
given by
the proposed
formula.
Temperature
g^ven by the
formula of
Messrs. Arago
and Dulong.
1
100
99-96
100
»»
214
123-7
123-54
123-34
99
2-8705
133-3
133'54
13317
»t
4
»*
145-43
144-88
tf
4-5735
149-7
150-39
149-79
149-77
It appears that the formula which we propose difiers from the
48 CHAPTER II.
These formulae, as well as other similar ones,
have the inconvenience of suiting only a limited part
of the scale of temperatures.
Among the formulae proposed by different authors
on the same subject, that of Southern is very suit-
able to steam formed xmder pressures inferior to that
of one atmosphere ; it deviates then from the truth
only in very low pressures, as appears from the
experiments of that engineer. But for pressures
superior to 1 atmosphere it ceases to have the same
accuracy : from 1 to 4 atmospheres it gives, in fact,
more error than that of Tredgold modified, and
above 4 atmospheres the error rises rapidly to 1 and
1 '5 degree of the centigrade thermometer, or 1*8 and
2*6 degrees of Fahrenheit ; so that the formula of
Messrs. Arago and Dulong, which is, besides, of
more easy calculation, becomes then far preferable
to it.
That of Tredgold modified, as well as that which
we propose to substitute for it, represent very
closely the observations for the interval between
1 and 4 atmospheres; but below that point they
are incorrect, and above it they are inferior in
point of accuracy to that of Messrs. Dulong and
Arago.
The latter accords remarkably well with the facts.
observed temperatures nearly as much as that of Tredgold modi-
fied ; but as the difierence from the observation is on the mtmw
side instead of the pkts, there results a coincidence at 4^ atmo-
spheres with that of Messrs. Arago and Dulong.
OF THE MECHANICAL ACTION Of THE STEAM. 49
from 4 atmospheres to 24. In this interval its
greatest difference with observation is -4 degree
of the centigrade thermometer or '7 of Fahrenheit,
and nearly all the other differences are only * 1 de-
gree centigrade or '18 Fahrenheit ; but, as we have
already said, it begins to deviate from the obser-
vation below 4 atmospheres.
No one, then, of these formulae suits the whole
series of the scale of temperatures, and to hold
exclusively to any one of them would be knowingly
to introduce errors into the Tables. As, moreover,
the true theoretic law which connects the pressures
with the temperatures is unknown, and as these
formulae are mere formulae of interpolation, esta-
blished solely from their coincidence with the facts,
the only right mode of making use of them is to
apply each respectively to that portion of the series
which it suits. Then, from the comparison of their
results with experience, one may rest assured that
the error on the temperature will in no point exceed
seven-tenths of a degree of Fahrenheit, or four-
tenths of a degree of the centigrade thermometer.
This is, therefore, the means we shall adopt in the
formation of the Tables we are about to present.
The formulae, which will serve to compose these
Tables, are then the following, which we present
here, not in their original terms, but transformed,
for greater convenience, into the measures usual
in practice ; that is, expressing the pressure p in
pounds per square inch or in kilograms per square
B
50 CHAPTER II.
centimetre, and the temperature ty in degrees of
Fahrenheit's, or of the centigrade thermometer,
reckoned in the ordinary manner.
Southern's formula, suitable to pressures less
than that of the atmosphere (English measures):
<=1557256 */y/|i- 04948-51 -3.
Tredgold's formula modified by M. Mellet, suit-
able to pressures from 1 to 4 atmospheres (English
measures) :
_/103+^\«
^ V20118>' '
<=201- 18/^11-103.
Proposed formula, suitable like the preceding, to
pressures from 1 to 4 atmospheres (English mea-
sures):
_/98^806-M\«
^ V 198-562 ^ '
<= 198-562 /^|i-98-806.
Formula of Messrs. Dulong and Arago, suitaUe
ta pressures from 4 to 50 atmospheres (English
measures) :
;)=(-26793-f 0067585 <)*,
<= 147-961 /^p-39-644.
Southern's formula, suitable to pressures less
than that of the atmosphere (French measures) :
OF THE MECHANICAL ACTION OF THE STEAM. 51
^=145-360*^1?- 0034542— 46-278.
Tredgold'8 fonnula modified by M. Mellet, suit-
able to pressures of 1 to 4 atmospheres (French
measures) :
^=174 /(/p- 75.
Proposed formula, suitable like the preceding, to
pressures from 1 to 4 atmospheres (French mea-
sures) :
_x72-67+<y
^ V 171 72 ^ '
^= 171-72 y^p-72-67.
Formula of Messrs. Dulong and Arago, suitable
to pressures from 4 to 50 atmospheres (French
measures) :
p= (•28658+0072003 <)*,
t= 138-883 /^-39-802.
Besides the formulae which we have just re-
lated, there exists another proposed by M. Biot,
which, compared by that illustrious natural phi-
losopher to the above-mentioned experiments on
high pressures, to those of Taylor on pressures
approaching nearer to 100 degrees centigrade, and
to a numerous series of manuscript observations
K
i>2 CHAPTBR II.
made by M. Gay-Lussac, from 100'' to — 20 de-
grees centigrade, reproduces the results observed,
with very sUght accidental deviations, such as the
experiments themselves are liable to. This formula,
which has consequently the advantage over the
preceding, of being appUcable to all points of the
scale, is the following :---
log. p=a-a,6.'*'*'-a,6,"^'.
Log. p is the tabulary logarithm of the pressure
expressed in millimetres of mercury at 0° centi-
grade ; / is the centesimal temperature counted on
the air thermometer, and the quantities a, a,, a,, b,,
bf, are constant quantities which have the following
values:
a - 5-96131330259,
log. a,= T-82340688193,
log. 6,= --01309734295,
log. o.= 74110951837,
log. 6,= -00212510583.
This formula cannot tail to be extremely useful
in many delicate researches on the effects of steam ;
but to establish, by its means, a Table of the form
we require, the pressure ought first to he deduced
from it for each degree of the air thermometer ;
then these degrees ought to be afterwards changed
into degrees of the mercury thermometer ; and as
Hiia would not give the temperatures corresponding
to given pressures, by regular intervals, a subsequent
nterpolation would be still necessary to make the
Table in the proper disposition. These long opera-
OF THE MECHANICAL ACTION OF THE STEAM. 53
tions induced us to give the preference to the pre-
viously cited formulae, for the construction of the
Tables which we shall shortly present.
Sect. II. Relation between the relative volumes
and the pressures, at equal temperature, or be-
tween the relative volumes and the temperatures,
at equal pressure, in the steam separated from
the liquid.
We have said that when the steam is in contact
with the generating liquid, its pressure is neces-
sarily connected with its temperature; and as the
density of an elastic fluid depends only on its
temperature and its pressure, it follows that the
density is then always constant for a given tem-
perature or pressure. But when the steam is
separated from the liquid, that connexion between
the temperature and the pressure no longer exists.
The temperature of the steam may then be varied
without changing its pressure, or reciprocally ; and
according as the one or the other of these two
elements is made to vary, the density of the steam
undergoes changes which have been an object of
investigation among natural philosophers.
One very remarkable law in the effects of gas
and steam is that which was discovered by Mariotte
or Boyle, and has since been confirmed, as far
as to pressures of 27 atmospheres, by Messrs.
Arago and Dulong. It consists in this, that if the
54 CHAPTER II.
volume of a given weight of gas or of steam be
made to vary without changing its temperature,
the elastic force of the gas will vary in the inverse
ratio of the volume it is made to occupy ; in other
words, in direct ratio of its density. That is to say,
if V and t/ express the volumes occupied by the
same weight of steam, and p and p' the pressures
which maintain the steam compressed under those
respective volumes, the temperature, moreover,
being the ^ame in both cases, the following analogy
will exist :
p ^v
"7 *" "~'
p V
And therefore, fi and ^' being the relative volumes
of the steam at the pressures p and p\ we shall have
p lu
According to this law, if a given weight of an
elastic fluid be compressed to half its primitive
volume, without changing its temperature, the
elastic force of that fluid will become double. But
it is plain that this efiect cannot take place in the
steam in contact with the liquid, because it supposes
that during the change of pressure the temperature
remains constant, whereas we have seen that in
such state, the pressure always accompanies the
temperature, and vice ^ersA,
Another property equally important in the ap-
OF THE MECHANICAL ACTION OF THE STEAM. 55
predation of the effects of steam has been discovered
by a celebrated chemist of our times, M. Gay-
Lussac. It consists in this, that if the temperature
of a given weight of an elastic fluid be made to vary,
its tension being maintained at the same degree,
it will receive augmentations of volume exactly
proportional to the augmentations of temperature ;
and, according to the latest experiments, for each
degree of the centigrade thermometer, the increase
of volume will be '00364 of the volume which the
same weight of fluid occupies at the temperature
zero. If the temperatures are taken from Fahren-
heit's thermometer, each augmentation of 1 d^^ree
in the temperature will produce an increase of
'00202 of the volume occupied by the fluid at the
temperature of 32°.
K then we call V the volume of the given weight
of the elastic fluid, under any pressure, and at the
temperature of 32 degrees of Fahrenheit, the volume
it will occupy under the same pressure, and at the
temperature t of Fahrenheit, will be
i;=V+Vx 00202 (^-32).
It follows that, between the volumes, v and v
occupied by the same weight of steam, at the same
pressure and under the respective temperatures
t and t\ there will be the following analogy :
t;_ 1+00202 U-32)
»'" 1+00202 U'-32)*
56 CHAPTER 11.
And since we have seen that the ratio between the
volumes occupied by the same weight of two dif-
ferent steams is no other than the ratio between
the relative volumes of those two steams, the two
preceding analogies will also be true, when we
replace the ratio of the two absolute volumes t; and
Vy by the ratio of the relative volumes ii and fi of
the steam.
This law, supposing that the temperature of the
steam changes, without the pressure undergoing
any change, obviously cannot apply to the effects
produced in steam in contact with the liquid, since
in such steam the pressure changes necessarily and
spontaneously with the temperature.
Sect. III. Relation between the relative volumes^
the pressures^ and the temperatures^ in the steam
in contact or not in contact with the liquid.
As it has just been observed, neither Boyle's
law nor that of Gay-Lussac can apply alone to
changes which take place in the steam remaining
in contact with the liquid. But it is clear that
from the two a third relation may be deduced,
whereby to determine the variations of volume
which take place in the steam, by virtue of a
simultaneous change in the temperature and in
the pressure; and this relation may then com-
prehend the case of the steam in contact with the
OF THE MECHANICAL ACTION OF THE STEAM. 57
liquid, since it will suffice to introduce into the
formulae the pressures and temperatures which,
in this state of the steam, correspond to each
other.
Suppose then it be required to know the volume
occupied by a given weight of steam, which passes
from the pressure |>' and temperature t\ to the
pressure f and temperature t. It may be supposed
that the steam passes first from the pressure 'p' to
the pressure p without changing its temperature,
which, from Boyle's law, will give between the
relative volumes of the steam the analogy
/^ =/* -;
V
then supposing this steam to pass from the tem-
perature i to the temperature f, without changing
its pressure, the relative volume of the steam, ac-
cording to the law of Gay-Lussac, will become
_ //I +00202 (^-32) _
^ ^ 1+00202 {i—2fl)
_ ,/ 1+00202 (^--32)
^p' 1+00202 (<'-32)'
This formula will then express the law according
to which the relative volume of the steam changes,
by virtue of a given combination of pressure and
temperature. Consequently, substituting in this
equation for f and ^, f' and t\ the pressures and
temperatures only which correspond to each other
58 CHAPTER II.
in the steam iii contact with the liquid, we shall
have the analogous changes which take place in
the relative volume of the steam, when it is not
separated from the water which generated it.
On the other hand, it is known by experience,
that under the atmospheric pressure, or 14*706 9bs.
per square inch, and at the temperature of 212° of
Fahrenheit's thermometer, the relative volume of
the steam in contact with the liquid is 1700 times
that of the water which has produced it. Hence
it is easy to conclude the relative volume of the
steam at any given pressure p and at the corre-
sponding temperature t. It suffices, in fact, to
insert the above values for p\ f^ and /, in the
general equation obtained above, and the result
will be
,„i700x. 14706 1+00202 (t^32)_
^ p ^1+00202x180
= 18329 1+00202 (<--32)
P
Thus we may, by means of this formula, cal-
culate the relative volume of the steam gene-
rated under a given pressiune, as soon as we know
the temperature answering to that pressure in
steam at the maximum of density for its tem-
perature.
It is what we have done in the construction of
the following Table. The second column has been
OF THE MECHANICAL ACTION OF THE STEAM. 59
formed by calculating the temperature of the steam
at the maximum density, from the formulae which
we have given in the first section of this chapter.
Then using this series of temperatures in the for-
mula which precedes, we have concluded the third
column, or the relative volumes of the steam in
contact with the liquid, under all the pressures
comprised between 1 and 8 atmospheres. This
Table will, in consequence, dispense with all cal-
culation with regard either to the research of the
temperatures, or to that of the relative volumes
of the steam; and its extent will suffice for all
applications that occur in the working of steam
engines.
When we speak of steam generated under a given
pressure, we understand the steam considered at the
moment of its generation, and consequently still
in contact witli the liquid. We have explained
elsewhere that the volume of the steam, compared
to that of the water which has produced it, is
precisely what we call the relative volume of the
steam.
60
CHAPTER II.
Table of the tenq^eraivre and volume of the steam gene-
rated under different pressureSy compared to the volume
of the water that has produced it.
Total pres-
sure, in
English
pounds per
square
inch.
Corre-
sponding
tempera-
ture, by
Fahren-
heit's ther-
mometer.
Relative vo-
lume,or volume
of the steam
compared to
the volume of
the water that
hasproducedit
Total pres-
sure, in
English
pounds per
square
inch.
Corre-
sponding
tempera-
ture, by
Fahren-
heit's ther-
mometer.
Relative vo-
lume,orvolume
of the steam
compared to
the volume of
the water that
hasproducedit.
1
102-9
20954
37
263-7
727
2
1261
10907
38
265-3
710
3
141-0
7455
39
266-9
693
4
152-3
5695
40
268-4
677
5
161-4
4624
41
269-9
662
6
169-2
3901
42
271-4
647
7
1760
3380
43
272-9
634
8
182-0
2985
44
274-3
620
9
187-4
2676
45
275-7
608
10
192*4
2427
46
2771
596
11
197-0
2222
47
278-4
584
12
201-3
2050
48
279-7
573
13
205-3
1903
49
2810
562
14
209-0
1777
50
282-3
552
15
2130
1669
51
283-6
542
16
216-4
1572
52
284-8
532
17
219-6
1487
53
286-0
523
18
222-6
1410
54
287-2
514
19
225-6
1342
55
288-4
506
20
228-3
1280
56
289-6
498
21
231-0
1224
57
290-7
490
22
233-6
1172
58
291-9
482
23
236-1
1125
59
293-0
474
24
238-4
1082
60
294-1
467
25
240-7
1042
61
294 9
460
26
243-0
1005
62
295-9
453
27
245-1
971
63
2970
447
28
247-2
939
64
298-1
440
29
249-2
909
65
299-1
434
30
251-2
882
66
300-1
428
31
253-1
855
67
301*2
422
32
255-0
831
68
302-2
417
33
256-8
808
69
303-2
411
34
258-6
786
70
304-2
406
35
260-3
765
71
305-1
401
36
2620
746
72
306*1
396
OF THE MECHANICAL ACTION OF THE STEAM. 61
Total pces-
sure, in
Sngliah
pounds per
aqnare
inch.
Corre-
sponding
tempera-
tnre, by
Fahren-
heH's ther-
mometer.
Relative vo-
lnme,or volume
of the steam
oompared to
the volume of
the water that
has produced it.
Total pres-
sure, in
En^ish
pounds per
square
inch.
Corre-
sponding
tempera-
ture, by
Fahren-
heit's ther-
mometer.
Relative vo-
lume,or volume
of the steam
compared to
the volume of
the water that
has produced it.
73
307- 1
391
92
323-5
317
74
3080
386
93
324-3
313
75
308-9
381
94
325-0
310
76
309*9
377
95
325-8
307
77
310-8
372
96
326-6
305
78
311-7
368
97
327-3
302
79
312-6
364
98
328-1
299
80
313-5
359
99
328-8
296
81
314-3
355
100
329-6
293
82
315-2
351
105
333*2
281
83
316-1
348
120
343-3
249
84
316-9
344
135
352-4
224
85
317-8
340
150
360-8
203
86
318-6
337
165
368*5
187
87
319-4
333
180
375-6
173
88
320-3
330
195
382-3
161
89
321 1
326
210
388*6
150
90
321-9
323
225
394-6
141
91
322-7
320
240
400-2
133
Sect. IV. Direct relation between the relative vo-
lumes and the pressures^ in the steam in contact
mth the li^id.
It has just been seen, from the formulae given
in the preceding section, that the density and
the relative volume of the steam, whether separated
from the liquid or not, are deduced from the know-
ledge of the simultaneous pressure and temperature.
It is likewise known that in the steam in contact
62 CHAPTER II.
with the liquid the temperature depends imme-
diately on the pressure. It should therefore be
possible to find a relation proper to determine
directly the relative volume of the steam in con-
tact with the liquid, or, in other words, of the
steam at the maximum density and pressure for
its temperature, by means of the sole knowledge
of the pressure under which it is formed.
The equation which gives the relative volume of
the steam in any state whatever, in terms of its
pressure and temperature, has been given above.
We have also shown the formulae which serve to
find the temperature in terms of the pressure, in
steam in contact with the liquid. Eliminating
then the temperature from the equation of the
volumes and that of the temperatures, we shall
obtain definitively the relation sought, or the rela-
tive volume of the steam at the maximum density,
in terms of the pressure only.
But here starts the difficulty. First, M. Biot's
formula not being soluble with reference to the
temperature, does not admit the necessary elimina-
tion. In the next place, the assemblage of the
three formulae presented above, which are made to
succeed each other, suit very well in the forma-
tion of tables of correspondence between the pres-
sures and the temperatures, when that is the end
proposed. Likewise, in an inquiry relative to the
expansion of the steam in an engine, when it is
known precisely within what limits of pressure
OF THB MECHANICAL ACTION OF THE STEAM. 63
that expansion will take place, it may immediately
be discerned which of the three formulae is ap-
plicable to the case to be considered, and then t may
be eliminated between that formula and the equation
of volumes. But if the question regards, for in-
stance, the case wherein the steam generated in
the boiler under a pressure of 8 or 10 atmospheres
might, according to the circumstances of the motion,
expand during its action in the engine, either to a
pressure less than 1 atmosphere, or to a pressure
between 1 and 4 atmospheres, or, in fine, to a pres-
sure superior to 4 atmospheres ; then we shall not
know which of the three formulae to use in the
elimination, and it will be impossible to arrive at
a general equation representing the effect of the
engine in all cases.
Besides, were we even to adopt any one of those
equations, the radicals they contain would render
the calculation so complicated as to make it unfit
for practical applications.
The equations of temperature hitherto known
cannot then solve the question that presents itself,
that is to say, satisfy the wants of the calculation of
steam engines in this respect; and, consequently,
the only means left is to seek, in a direct manner,
an approximate relation, proper to give immediately
the relative volume of the steam at the maximum
density in terms of the pressure alone.
With this view M. Navier had proposed the
expression :
64 CHAPTER II.
1000
•09 + 0000484 p •
in which fi is the relative volume, or the ratio of the
volume of the steam to that occupied by the same
weight of water, and p the pressure expressed in
kilograms per square metre.
It would be easy to transform this formula into
English measures; but as it deviates considerably
from experience for pressures below the atmosphere,
and therefore was never intended to apply to con-
densing engines; and as, moreover, for non-con-
densing or high pressure engines, it is not nearly
so exact as the formula which we are going to
propose, we shall only present here the last one
in English measures.
Formula for high pressure engines :
10000
''"" 1-421 +0023p'
In this expression fi represents the relative volume
of the steam, and p is its pressure expressed in lbs.
per square foot.
To give a precise idea of the approximation given
by this formula, we here subjoin a Table of the
values it furnishes for the principal points of the
scale of pressures. It will be remarked that in high
pressure engines, the steam can hardly be spent at
a total pressure less than two atmospheres, by
reason of the atmospheric pressure, the friction of
the engine, and the resistance of the load. Therefore
OF THE MECHANICAL ACTION OF THE STEAM. 65
it is needless to require of the formula exact vo-
lumes for pressures less than two atmospheres.
Relative volume of the steam generated under different
pressures f calculated by the proposed formula.
Volume calcula-
Total pressure
of the steam, in
pounds per square
inch.
Volume of the
steam, calculated
by the ordinary
formuhe.
ted by the pro-
posed formula for
high-pressure
non-condensing
engines.
15
1669
>>
20
1280
1243
25
1042
1031
30
882
881
35
765
768
40
677
682
45
608
613
50
552
556
55
506
509
60
467
470
65
434
436
70
406
406
75
381
381
80
359
358
85
340
338
90
323
320
105
281
276
120
249
243
135
224
217
150
203
196
Sbct. V. Of the constituent heat of the steam in
contact with the liquid.
There is yet an inquiry, relative to the properties
of steam, which has long fixed the attention of
natural philosophers : it is that of the quantity of
heat necessary to constitute the steam in the state
F
66 CHAPTER II.
of an elastic fluid under various degrees of elas-
ticity.
It is well known that when water is evaporated
under the atmospheric pressure, in vam new quan-
tities of heat may be added by means of the fur-
nace ; neither the temperature of the water, nor that
of the steam, ever rise above 100° of the centigrade
thermometer, or 212° of Fahrenheit. All the heat
then which is incessantly added to the liquid must
pass into the steam, but must subsist there in a
certain state which is called latent^ because the
heat, though really transmitted by the fire, remains
nevertheless without any efiect upon the thermo-
meter, nor does it afterwards become perceptible
till the moment of disengaging itself, on the steam
being condensed.
This latent heat evidently serves to maintain the
molecules of water in the degree of separation suit-
able to their new state of elastic fluid; and it is
then absorbed by the steam, in a manner similar
to that which is absorbed by the water, on passing
from the solid state, or state of ice, to the Uquid.
But it is important to know the quantity of the
latent heat, in order to appreciate with accuracy
the modifications the steam may undergo.
Some essays made by Watt had already elicited
that the steam, at the moment of its generation,
or in contact with the liquid, contains the same
quantity of total heat, at whatever degree of tension,
or, in other words, at whatever degree of density,
OF THE MECHANICAL ACTION OF THE STEAM. 67
it may be formed. The experiments of Messrs.
Sharpe and Clement have since confirmed this re-
sult. From them is deduced, that the quantity
of latent heat contained in the steam in contact
with the liquid is less and less, in proportion as
the temperature is higher; so that the total heat,
or the sum of the latent heat plus the heat indicated
by the thermometer, forms in sdl cases a constant
quantity represented by 650° of the centigrade ther-
mometer, or, 1 1 70° of Fahrenheit's.
Southern, on the contrary, has concluded from
some experiments on the pressure and temperature
of steam, that it is the latent heat which is con-
stant ; and that, to have the total quantity of heat
actually contained in steam formed at a given tem-
perature, that temperature must be augmented by
a constant number, representing the latent heat
absorbed by the steam in its change of state.
Some authors have deemed this opinion more
rational, but the observations we are about to
relate seem to us to set the former beyond all
doubt.
It is known, that when an elastic fluid dilates
itself into a larger space, the dilatation is invari-
ably attended with a diminution of temperature.
If, then, the former of the two laws be exact, it
follows that the steam, once formed at a certain
pressure, may be separated from the liquid, and
provided it lose no portion of its primitive caloric,
68 CHAPTER II.
by any external agent, it may dilate into greater and
greater space, passing at the same time to lower and
lower temperatures, without ceasing on that account
to remain at the maximum density for its actual
temperature. In effect, since we suppose that the
steam has in reality lost no portion of its total heat,
the consequence is, that it always contains precisely
as much as suffices to constitute it in the state of
maximum density, as well at the new temperature
as at the former.
If, on the contrary, Southern's law be exact,
when the steam, once separated from the liquid,
will diminish in «[ensity as it dilates into a larger
space, it will not remain at the maximum density
for the new temperature. To admit indeed that it
would do ^o, would be to verify Watt's law, since
the new steam would be at the maximum density,
although containing precisely the same quantity
of total heat as the old. But since we admit, on
the contrary, that the primitive steam contained
more heat than was necessary to constitute the new
at the maximum density, it follows that the surplus
heat, now liberated, will diffuse itself in the new
steam; and as this is separated from the liquid,
the increase of heat cannot have the effect of in-
creasing the density of the steam, but will be alto-
gether sensible in the temperature. Thus the
result will be, a steam at a certain density, indi-
cated by the spaces into which it is dilated, and
OF THB MECHANICAL ACTION OF THE STEAM. 69
at a temperature higher than what is suitable to
that density, in steams at the maximum of density
for their temperature.
Now, in a numerous series of experiments, of
which we shall speak hereafter, we have found
that in an engine whose steam-pipes were com-
pletely protected against all external refrigeration,
the steam was generated at a very high pressure
in the boiler; and, after having terminated its
action in the engine, escaped into the atmosphere
at pressures very low and very varied ; and that in
every case the steam issued forth precisely in the
state of steam at the maximum of density for its
temperature. Southern's law then is inadmissible,
unless any one choose to suppose that in these
varied changes of pressure the steam lost, by
contact with the very same external surfaces, al-
ways precisely and strictly just that quantity of
heat, sometimes very considerable, at other times
very small, by which its temperature should have
increased. Consequently the law of Watt is the
only one supported by the facts.
The total quantity of heat contained in the steam
in contact with the liquid, and under any pressure
whatever, is then a constant quantity ; and accord-
ing as the sensible heat increases, the latent heat
diminishes in an equal quantity.
On the other hand, according to the same law,
if we conceive water to be enclosed in a vessel
capable of sufficient resistance, and submitted to
70
CHAPTER 11.
temperatures of greater and greater intensity; the
latent heat of the steam thence arising will be less
and less as the sensible heat or temperature shall
become greater ; and as soon as the steam shall be
generated at a temperature equal to 650® centigrade
or 1170° of Fahrenheit, it will cease to absorb
heat in a latent state, and will no longer receive
any portion of it, but which will be sensible on
the thermometer. We must then conclude that
at this point the steam will have a density equal
to that of water ; since in passing from one state
to another, it requires no farther increase of caloric,
as would be necessary if any farther increase of se-
verance were to take place between the molecules.
Thus the water, though still contained in the vessel,
will all have passed into the state of steam, so that
there will be no more steam in contact with the
liquid. From this moment, then, new quantities of
heat may be applied to the vessel ; but instead of
acting on a liquid, which passes to the state of gas,
by absorbing latent heat, it will now only act on an
elastic fluid, and therefore all the increase of heat
will, as in all gases, become sensible on the ther-
mometer.
This observation explains the difficulty which
would otherwise present itself; viz., that beyond
650° centigrade or 1170° of Fahrenheit, the pre-
ceding law could not subsist without the latent
heat becoming a negative quantity, which is im-
possible.
OF THB MECHANICAL ACTION OF THE STEAM. 7l
Sect. VI. — Of the conservation of the maximum
density of the steam for its temperature ^ during its
action in the engine.
When an engine is at work, the steam is gene-
rated in the boiler at a certain^ pressure ; from
thence it passes into the cylinder, assuming a dif-
ferent pressure, and then, if it be an expansive
engine, the steam, after its separation from that of
the boiler, continues to dilate itself more and more
in the cylinder, till the end of the stroke of the
piston. It is commonly supposed that, during all
the changes of pressure which the steam may un-
dergo, its temperature remains the same, and the
consequent conclusion is that, during the action of
the steam in the engine, its density or relative vo-
lume follows the law of Boyle or Mariotte ; that is
to say, the relative volume varies in the inverse
ratio of the pressure. This supposition simplifies
indeed the formulae considerably, but we shall pre-
sently see that it is contrary to experience ; and
therefore it becomes necessary to seek what is the
true law, according to which the steam changes
temperature in the engine, at the same time that its
pressure changes. And as calculations relative to
the effects of steam depend essentially on the
volume it occupies, we must seek also what changes
that volume undergoes, by reason of the variations
of temperature and pressure which take place in
the steam during its action.
72 CHAPTER II.
We shall then substitute for the relation pre-
cedently indicated, according to Mariotte's law,
another more real, and, what is essentially necessary
to calculate the effects of steam with accuracy,
deduced from the facts themselves.
We have just^ said that the calculations relative
to steam engines suppose the steam to preserve
invariably its original temperature, which allows
the application of Boyle's or Mariotte's law to
all the changes of density or of pressure it may
undergo. However, as it is known that elastic
fluids never dilate without cooling in some degree,
this supposition obviously could not be realized, but
on condition that the steam have time to recover
from the bodies with which it is in contact, sup-
posed to be* sufficiently heated, the quantity of
caloric necessary to restore its temperature, after
expansion, to the same degree at which it was
before. Now, the rapidity of the motion of the
steam in the cylinders and the pipes, and the
natural temperature of those pipes, which makes
them rather liable to take caloric from the steam
than to supply it with caloric, will not suffer the
admission of such an hypothesis.
To obtain satisfaction on this head, in a numerous
series of experiments, we adapted to the boiler of a
locomotive engine a thermometer and an air-gauge
or manometer ; we appUed also two similar instru-
ments to the pipe through which the steam, after
having terminated its action in the engine, escaped
OF THE MECHANICAL ACTION OF THE STEAM. 73
into the atmosphere ; and we observed their simul-
taneous indications. The steam was generated in
the boiler at a total pressure varying from 40fl>s. to
65fts. per square inch, and escaped into the atmo-
sphere at a pressure varying, according to different
circumstances, from 20fts. to 15fl>s. per square
inch. Had the steam preserved its temperature
during its action in the engine, it would have issued
forth with the pressure, for instance, of 1 5 fl>s. per
square inch, but with the temperature proper to the
pressure at which it had been formed, that is, 65fts.
per square inch. Now, nothing Uke this took place :
during some hundreds of experiments wherein we
observed and registered these effects, we found in-
variably that the steam escaped precisely with the
temperature suitable to its actual pressure.
In effect, the divisions of the thermometer em-
ployed indicated the pressure in steam in contact
with the Uquid ; that is to say, the degrees of
temperature having been first marked in the ordi-
nary way, the temperatures had been afterwards
replaced, from known Tables, by the corresponding
pressures in steam at the maximum of pressure or
of density for its temperature. This instrument
m
showed then at every moment the maximum pres-
sure corresponding to the actual temperature of the
steam. On the other hand, the air-gauge measured
directly the real pressure of the steam. The two
instruments then could agree only so long as the
real pressure of the steam was at the same time the
74 CHAPTER II.
maximum pressure corresponding to the tempe-
rature of that steam. But, during the whole course
of the experiments, the thermometer was found to
give identically the same degree of pressure as the
air*gauge, and it equally agreed with a siphon-
manometer which we had superadded to the appa-
ratus at the point of the outlet of the steam. The
steam then was generated in the boiler at a certain
very high pressure, and quitted the engine at a
very low one ; but, on its leaving the engine, as
well as at the moment of its production, that steam
was at the maximum of pressure or of density for
its temperature, that is to say, it was precisely in
the same state in which it would have been, had it
risen immediately from the liquid at its actual
pressure.
We will not relate all the experiments in which
we have observed this result, since it would be a
mere repetition of the same thing, and since, in
order at the same time to attain other determi-
nations relative to the engine, and particularly that
of the pressure due to the blast-pipe, as will here-
after appear, we necessarily made a very great
number of observations on the subject ; but to give
an idea at least of the results, we will present a
few series of them in the following Table :
OF THE MBCHAXICAL ACTION OF THE STEAM
#D
EjrperimemiB am the changes of pressure and ten^prrature
of the steamk, Atring its action in the engine.
Total prescareof
the suaiBv in ft*^
: per iq. iBch, txt
thff ■KHDCBl of(
its gcjitiaiioB in
thehoilrr^bTtbe
air-fuige aiid by
tlie thenDometer. .
1
1
•
1
Toul pressaiv of tb«
fteam, in lbs. per sq. ,
incb, at the moment oi ',
I
CormpoBding
temperature, in
decrees o€
Fahn^nheit*s
thermonieter.
tnnpcnture, |
Fahrenheit'i
thomoiDCier.
its leaving the cmpmt,
by the jbr the tber-
air-fange. momcter. ■
59
293
16-5
16-5 1
218
GO
2941
16-5
16 5
218
61
294-9
16-5
16-5
218
63
297
16-5
16-5
218
62
295-9
17-5
17-5
2211
61
294-9
18-5
185
2241
61
294-9
19-5
19-5
226 9
59
293
19-5
19-5
226-9
59
293
20-25
20-25
229
59
293
20-5
20-5
229-6
59
293
20-25
20-25
229
46
2771
18
18
222-6
49
281
18-5
18-5
224-1
54
287-2
20
20
228-3
56
289-6
21
21
231
51
283-6
21-5
21-5
282-3
51
283-6
21-25
21-25
231-6
53
286
20-5
20-5
229-6
52
284-8
19
19
225-6
51
283-6
19
19
225-6
52
284-8
19
19
225-6
51
283-6
19
19
225-6
1 51
283-6
18-5
18-5
224- 1
53
286
18-5
18-5
224- 1
54
287-2
18-5
18-5
224- 1
57
290-7
18-5
18-5
224- 1
58
291-9
18-5
18-5
2241
62
295-9
17-25
17-25
220-3
64
2981
17-75
17-75
221-8
62
295-9
18
18
222-6
61
294-9
18-75
18-75
224-8
64
298-1
21-5
21-6
232*3
60
294- 1
^1-5
21-5
232*3
60
294- 1
20-75
20-75
230-3
61
294-9
20-75
20-75
230-3
62
295-9
21-25
21-25
231-6
63
297
21-75
21-75
232*9
76 CHAPTER II.
We see from these experiments, that the steam,
after having been generated in the boiler at a very
high pressure and temperature, lowered its pressure
more or less in the engine, but that its temperature
lowered at the same time, and in such sort that the
steam was always at the maximum of pressure or of
density for its temperature.
In the engine submitted to experiment, the
steam, throughout its action, was completely pro-
tected against all external refrigeration; for the
pipe which conducted it from the boiler to the
cylinder was immerged into the steam of the boiler
itself, as far as the point where it entered the
smoke-box. Then, as well in the interval which
separates that point from the entrance of the cy-
linder as during its action in the cylinder itself, and
from its quitting the cylinder to the orifice of the
blast-pipe, the steam was continually traversing
passages entirely enclosed in the smoke-box, and
consequently in immediate contact with the flame
and hot air proceeding from the furnace. The steam
could not then be liable to any external refrigera-
tion.
The above-mentioned experiments referred then
to an engine perfectly guarded against any external
refrigeration. On the other hand, supposing an
engine wherein these external causes of refrigeration
were not provided against, the effect will be first to
operate the condensation of a part of the steam
produced, and there will consequently exist in the
OF THE MECHANICAL ACTION OF THE STEAM. 77
passages traversed by the steam a certain quantity
of ¥rater in its liquid state. It will be precisely the
same in the cylinder of a condensing engine, after
the imperfect condensation of the steam. In each
of these two cases, the remaining steam will be
found materially in presence of the liquid, and
consequently will again be necessarily at the maxi-
mum of density for its temperature.
Finally, a third case might be supposed, that in
which the steam should, on the contrary, acquire
heat after its separation from the water of the
boiler. Then, contrary to what has been seen to
take place in the locomotive engine mentioned
above, it is plain that the steam would acquire a
temperature above that which is proper to steam at
the maximum density for its temperature ; but this
case does not occur in steam engines, and it will
therefore be useless to dwell on it.
It is consequently to be concluded from the fore-
gping, that in steam engines more or less perfectly
guarded against all external refrigeration, the steam
remains always, during its action in the engine, in
the state of maximum density for its temperature,
as if it had never ceased to be in contact with the
generative liquid.
Now, we have shown in the fourth section of this
chapter, that, with regard to steam in contact with
the liquid, the relative volume may be expressed in
terms of the pressure by a very simple formula,
which we may present generally under the form
78 CHAPTER II.
n+qp
This analogy, in which n and q will have the nume-
rical values already indicated, will then be applicable
to all the changes of volume of the steam during its
action in the engine.
From this equation, if we suppose that a certain
volume of water, represented by S, be transformed
into steam at the pressure p, and that we call M the
absolute volume of steam which will be produced by
it, we shall have
S «+?p
If afterwards the same volume of water be trans-
formed into steam at the pressure p\ and that we
call M' the absolute volume of the resulting steam,
we shall have also
M' 1
S n+jp'
Consequently, between the absolute volumes of
steam which correspond to the same weight of
water, we shall have the definitive relation,
M n ,
-+P
9
that is to say : the volumes of the steam will be,
not in the inverse ratio of the pressures, as was
supposed in admitting Boyle's or Mariotte's law,
OF THE MECHANICAL ACTION OF THE STEAM. 79
but in the inverse ratio of the pressures augmented
by a constant quantity.
From the equation (6) is likewise drawn the
analogy
And the two equations (6) and (c) will serve to
determine, either M, or p^ accoi^ing to the one of
these two quantities, which will be unknown.
As, in all calculations relative to the effects of
steam engines, the volume occupied by a given
weight of steam forms the important element of the
calculation, it is very obvious that the use of the
principle of the conservation of the maximum density
of the steam for its temperature ^ during its action in
the engine, and the formulae by which we have
represented it, will tend to the avoiding of many
considerable errors in the results.
If we consider a condensing engine in which the
steam generated at the pressure of 8 atmospheres,
or 120 fts. per square inch, shall expand to lOfts.
per square inch ; then, in the usual mode of calcula-
tion, it will be supposed that the steam, diuing its
expansion, will preserve its temperature, and that
its volume will vary in the inverse ratio of the
pressures. The volume of the steam at the pres-
sure of 120 lbs. per square inch is 249 times that of
the water which produced it. If its temperature
remained unchanged during its action in the engine,
its volume after the expansion would become
80 CHAPTER II.
249 X ^ =2988.
The supposition, then, amounts to admitting that
under the pressure of 10 lbs. per square inch, the
volume of the steam would be 2988 times that of
the water. Now, from accurate Tables, this volume
is 2427. An error, then, is induced of ^ on the real
volume of the steam, that is to say, on the effect of
the engine ; and this error will be almost entirely
avoided by the use of our formula suitable to con-
densing engines {Theory of the Steam Engine^ chap.
II. sect, iv.), since it gives in this case 2417, in-
stead of 2427, that is to say, it differs inconsiderably
from the true volume of the steam.
In non-condensing engines, the error which re-
sults from the application of Mariotte's law is again
very sensible, though less considerable than in the
preceding engines. If, in fact, we suppose an engine
wherein the steam be generated at the pressure of
5 atmospheres, or 75Ibs. per square inch, and ex-
pended at the pressure of 30fts. per square mch, or
about 2 atmospheres, as the volume of the steam
formed under the pressure of 75 lbs. per square inch
is 381 times the volume of the water, it is plain
that, if the action of the steam took place without
the temperature changing, its volume, at the moment
of its action, would be represented by the number
381 X 1=952.
But from exact Tables, the volume of the steam
formed at the pressure of 30fts. per square inch is
OF THE MECHANICAL ACTION OF THE STEAM. 81
really 882 times the volume of the water. Ad-
mitting, by the fact, the former number instead of
the latter, an error will be committed of about ^ on
the real volume of the steam, and consequently on
the effect of the engine ; and that error will be
totally avoided by using the Tables which we have
given of the volume of the steam. Using our
formulae for non-condensing engines, the resulting
number for the volume of the steam will be 881
instead of 882. In this case also will thus be
avoided the above-mentioned error.
We must however add, that with respect to slight
differences of pressure, such as occur in a great
number of cases, the error resulting from the use of
Mariotte's law may become quite unnoticeable.
Q
CHAPTER III.
OF THE PRESSURE OF THE STEAM. IN LOCOMOTIVE
ENGINES.
ARTICLE I.
OF THE SAFETY-VALVES.
Sect. I. Of the Pressure calculated according to the
Levers and the Spring -balance.
When an elastic fluid is confined in a closed
vessel, it produces in every direction, on the sides
of the vessel, a pressure, which is the result of its
elastic force, and which gives the exact measure of
that force. If, the vessel being already filled with
steam, a fresh quantity is continually added, the
elastic force of the steam will augment more and
more, and consequently also the pressure it produces
on every square inch of the surface of the vessel.
Now if at one point of the vessel there be a valve,
that is to say, an aperture, closed with a moveable
piece supporting a certain weight, it is clear that, as
soon as the steam contained in the vessel produces
upon the moveable plate a pressure equal to that
of the weight which holds it down in the opposite
OF THE PRESSURE. 83
direction, the plate will begin to be lifted up ; the
passage will then be opened, and the steam escaping
through the aperture, will show that its pressure was
greater than the weight that loaded the plate or
valve.
It must however be observed, that the resistance
which opposes the egress of the steam does not
consist only in the weight that has been placed on
the valve. Besides that weight, the atmosphere
produces also on the valve a certain pressure, as
well as upon every other body with which it comes
in contact. That pressure is known to be equal
to 14"7ibs. per square inch. It is therefore the
weight, added to the pressure of the atmosphere,
that gives the real measure of the elastic force of
the steam ; while the weight alone represents only
the surplus of the pressure over the atmospheric
pressure, or what is called the effective pressure of
the steam. Consequently, when a valve has a sur-
face of five square inches, and supports a weight of
250fl>s., which, divided between the five square
inches, gives a resistance of 50 lbs. per inch, that
amoimt of 50 fl>s. expresses the effective pressure of
the steam, a valuation frequently made use of on
account of its convenience for calculation, whereas
64*7 fl>8. is the real resistance opposed, and therefore
the real pressure of the steam.
On this principle are grounded the means of
measuring the pressure in steam engines, but in-
stead of imposing directly a weight on the valve.
84 CHAPTER III.
which weight must needs be considerable, a lever is
used; and as moreover a heavy body suspended
at the extremity of such lever would be liable to
continual jerking, during the motion of the en-
gine, which would cause an incessant opening and
shutting of the valve, this weight is replaced by an
equivalent spring.
Figure 1 6 represents the apparatus used in loco-
motive engines. The point C is a fixed pivot round
which the lever CB may move up and down. At
the point A this lever presses on the valve S by
means of a pin, and is held at its extremity B by
the above-mentioned spring. This consists of a
spiral, which by being more or less compressed, is
able to support in equilibrium, and consequently to
represent, larger or smaller weights. In other words,
it is a spring-balance, such as is used for weighing
in daily occurrences.
This balance consists of a rod T (fig. 16) which
is held in the hand, and to which is fastened a plate
with a narrow oblong aperture in it. Behind this
plate, and in a cylindrical tube, is a spring, the foot
of which rests on the basis L, which is fixed to the
plate. At its other end, this same spring is pressed
by a moveable transverse bar mn. At the inferior part
of the apparatus is a rod P, to which are fastened the
objects that are to be weighed. The prolongation of
the bar mn projects through the aperture of the plate,
and is terminated by an index which appears on the
outside, and which slides up and down the aperture in
OF THB PRESSURE. 85
proportion as the spring is more or less compressed.
Divisions are engraved along that same aperture. In
order to mark them, known weights of lib., 2 lbs.,
&e. are successively suspended at P, and according as
those weights, by pressing on the sprmg, cause the
index to rise, the corresponding divisions are marked.
The consequence of this is, that when an object
of unknown weight is suspended at P, and makes
the index rise to the point marked 10, that is to
say, to the same point to which a known weight of
lOfts. made it rise, we conclude that the object also
weighs lOfts. This is the sort of balance which is
used for measuring the pressure in locomotive en-
gines. We see that, by taking it off from the engine,
and suspending known weights to it, the divisions
may easily be verified, after the balance is graduated.
On the engine, the foot P of the balance, where
the object to be weighed would be suspended, is
fixed in a solid manner to the boiler ; and the rod
T, which would be held in the hand in common
weighing, is fastened to the end of the lever. This
rod passes through an aperture cut through the end
of the lever, and is fixed above it by a screw which
rests upon the lever. When it is required that this
balance shall produce a pressure of 10 lbs., nothing
more is necessary than to lower the screw until the
spring rises to the point marking 10 lbs., and the
same for any other weight.
Vice versd^ the steam being in the boiler at an
unknown degree of pressure, if we loosen gradually
86 CHAPTER III.
the screw until the steam begins to raise the valve,
that is to say, until its pressure stands in equilibrio
with the pressure of the spring, the pressure of the
steam will be known, for the degree then marked
by the index will show the weight which is equal
to it.
Kiiowing the weight marked on the balance, or
represented by the tension of the spring, it is easy
to deduce the resulting pressure on the valve per
unit of surface ; for the weight multiplied by the pro-
portion of the two arms of the lever gives, firstly,
the total pressure on the whole valve, and this di-
vided by the area of the valve gives the pressure
acting on each unit of its surface. Thus P being
the weight inscribed on the balance, its effect on the
point A will be
BC
PX
AC
and if the area of the valve be expressed by a, the
pressure on the unit of surface will be
^AC
p = —
a
To avoid all necessity of calculation in this respect,
the lever is often so constructed that the ratio of its
two parts is expressed by the number itself which
expresses the surface of the valve. That is, if the
area of the valve is 5 square inches, the levers will
be made in the proportion of 5 to 1 ; then the pres-
OF THK PRESSURE. 87
sure per unit of snriaoe of the valve is immediately
given by the weight inscribed on the balance.
If, for instance, we suppose a valve of 2^ inches
in diameter, which makes very nearly 5 square
inches of sur£aux, and that the two levers BC and
AC be 15 inches and 3 inches, a weight of 50fts.
marked on the balance will, from the ratio of the
levers, act on the valve with a pressure of 5 times
50^8., or 250 fts., which, divided among the 5
square inches of surfece of the valve, will give
50 fts. per square inch, which is precisely the weight
marked on the balance.
Sect. II. Of the corrections to be made to the weight
marked by the Spring -balance.
The calculation explained above gives the pressure
acting on the valve. However, it will easily be con-
ceived, by the manner in which the spring-balance
acts upon the valve, that, to know the pressure
which really opposes the egress of the steam, it is
not sufficient to read the degree where the index
stops, and to calculate the effect produced at the end
of the lever, as we have done above. In fact, first,
besides the weight represented by the spring, and
which would be suspended at the end of the lever, it
is clear that the weight of the lever itself causes a
certain degree of pressure ; for before the steam is
able to act on the spring, it must raise the whole
weight of the lever. The same takes place in regard
I
88 CHAPTER III.
to the disk of the valve, which must be raised before
the steam can have anv action on the balance. —
2. When any object is weighed with the hand, that
object is suspended at the lower part of the balance,
but then the hand supports the upper part, that is to
say, the rod, with the spring to which it is fastened;
and that effort is not taken into account, because
it does not make a part of the weight. Here, on
the contrary, the rod, the screw, and the spring, are
an additional weight really suspended at the end of
the lever, over and above the pressure marked by
the spring ; they must all be raised before the spring
can be pressed upon in any way, and can register
any effort; they must therefore be taken into ac-
count. The true pressure which takes place on the
valve will consequently not be known, until are
added to the weight marked in the balance : 1 . The
pressure produced by the weight of the lever at the
place of the valve ; 2. The pressure produced at the
end of the lever by the weight of the rod and spring
of the balance.
To measure at once these two additional resist-
ances, the following means may be used. First
loosen completely the screw of the balance, till the
spring no longer pulls on the lever, and till the valve
bears no other weight than that of the lever itself,
and its dependent apparatus. Then pass a string
round the pivot A which rests on the valve, and
having attached the extremities of this string to
another spring-balance, raise the whole with the
OF THE PRESSURE. 89
hand, by means of this second balance, till you see
the index of the balance of the engine stop at zero
of weight. The additional weight sought will be
indicated on the balance borne in the hand. It is in
fact clear that, by this proceeding, all the additional
weight on the valve is held in equiUbrio, and that if
the valve could be maintained in this state while at
work, every pound of pressure in the boiler would
immediately mark one pound of pressure on the
balance, since there would no longer be any addi-
tional weight to raise.
By this means, then, may be known the addition
that ought to be made to the pressure indicated by
the balance. It is found that, when the levers are
36 inches in total length, of a usual thickness and
with the balance commonly adapted to them, they
produce on the valves an additional pressure of 7 to
8 lbs. per square inch, and when they are 15 inches
in total length with their corresponding apparatus,
the additional pressure still amounts to 3 or 4 lbs.
per square inch. This therefore is obviously a cor-
rection not to be neglected, if in the calculation a
certain degree of accuracy be required.
Finally, there is another cause of error which it is
proper to note here.
In order that the valves may exs^^ctly close the
opening to which they are applied, without being
subject to contract an adhesion with the seat that
supports them, it is necessary to make them slightly
conical, or at least with a slanting border, as repre-
90 CHAPTER III.
sented in figs. 20 and 22. When these valves rest
upon and completely fill their seat, it is very clear
that the steam can only act upon their inferior sur-
face; consequently, the area which we have ex-
pressed ahove by a, must be taken after the inferior
diameter of the valve. To be perfectly exact, this
area ought even to be taken from the diameter of the
orifice covered by the valve, for the latter might be
constructed in the form of fig. 2 1 , where it is seen
that the surface according to which the pressure is
to be divided, is not ah but cd. Taking then the
proper measurements, and calculating as we have
done above, the exact pressure will be found for
every case in which the valve rested upon the seat,
or, if raised, was raised only for an instant, and
in a very small degree ; but whenever the steam,
being generated in greater quantity than it is ex-
pended by the cylinders, escapes with force through
the valve, it raises considerably the disk of the
valve: the consequence then is, that, instead of
acting merely on the inferior surface of the valve,
it evidently acts on a greater surface, and which
is still greater the more the valve is raised.
The efiect of this alteration in the diameter of
the valve, which at first sight appears triflmg, is
in fact very considerable. Let us suppose, for in-
stance, that we have a valve of 2*50 inches in dia-
meter at the bottom, and 3 inches at the top. Let
us further suppose that, by the efiect of the blowing
of the steam, the valve has been raised so as to
OF THE PRESSURE. 91
have increased its real diameter onlv bv one-ei^rhth
of an inch ; the surface of the valve, which was at
first
4 '91 square inches,
has become
5"41 square inches.
Consequently, if we supjxjse the total weight sup-
ported by the valve to be 245 lbs., that weight,
when the valve is shut, will represent a pressure
per square inch of
245
and when the valve is raised, that same weight will
only represent a pressure of
245
3:^ = 45-27 lbs.
The above established calculation, then, is to be
depended on only, when the balance-screw can be
lowered so as precisely to equilibrate the interior
pressure, as has been said above, without, however,
allowring the valve to rise. But the thing is not
possible when the engine produces a surplus of
steam beyond what its cylinders can expend, be-
cause this steam must necessarily have an issue.
In this case, then, the pressure is to be found only
by recurring afterwards to the barometer-gauge, as
we shall presently indicate.
92 CHAPTER III.
ARTICLE II.
OP THE INSTRUMENTS SPECIALLY DESTINED TO
MEASURE THE PRESSURE.
Sect. I. Of the Barometer-gauge ^ or Syphon-
manometer.
The calculiitions just proposed can only be es-
tablished by measuring and weighing divers parts
of the engine, which requires time and care, and
can be effected only when the machine has ceased
working. The great utility then is obvious of an
instrument which, at once and by the mere inspec-
tion, shall give the exact measure of the pressure of
the steam. With the aid of such an instrument, no
case, not even that of the raised valve, opposes the
smallest difficulty, nor needs any calculation.
Several instruments have been imagined for this
purpose. The syphon-manometer, which we shall
notice first, is represented in fig. 18. This instru-
ment is not portative, for which reason those we
shall describe in the following sections, and which,
moreover, are much less expensive, will of course
be preferred to it for the use of locomotives. How-
ever, as the manometer is the most accurate for
the engine at rest, and as it may also serve for
the graduation and verification of the others, its
construction shall be shown here.
The instrument is established on the same prin-
OF THE PRESSURE. 93
ciple as the common barometer. Mbm is a tube
containing mercury, which ought not to rise above
the two points M and m. FG is a water reservoir,
the use of which is to keep the branch Mb con-
stantly full of water, in proportion as the mercury
descends in that branch. Its diameter is purposely
much greater than that of the tube, in order that
the upper level of the reservoir be not sensibly
lowered by reason of the water which « it supplies to
the tube. That level ought not to rise above the
cock E, the use of which is to get rid of the surplus
of water that may have been produced by condensa-
tion on some former experiment. R is an opening
closed by a cock, and through which mercury or
water may, when wanted, be introduced into the
instrument. Lastly, C is a tap on which a tube
is screwed, the other end of which reaches the
boiler of the engine. This tube is flexible, and
usually made of tin ; it forms the commimication of
the mercurial-gauge with the engine. At the point
where it reaches the engine, it is screwed on a tap
fixed to the boiler, and kept close by a cock.
To prepare the instrument for use, an additional
quantity of mercury is poured into it by the aperture
R, in order to be sure that the instrument contains
mercury at least to the height Mm. After this, the
screw-bolt M is unscrewed, so that if there happen
to be too much mercury it may run off. When
this is done the screw-bolt is replaced, and an addi-
tional quantity of water is also poured through R
94 CHAPTER III,
into the reservoir FG, and, should there be too
much, it is also allowed to run off through the cock
E. Then the instrument is put in communication
with the boiler. The steam, arriving through the
tube C in the upper part of the reservoir FG, presses
on the water by virtue of its elastic force ; it con-
sequently presses the mercury down in the branch
M&, and makes it rise in the branch mb which is
open at the top, until the weight of the mercury,
thus raised, is equal to the pressure of the steam
issuing from the boiler. A metal float borne on
the surface of the mercury, at the point m, rises
in proportion as that surface rises in the tube;
and an index suspended to a thread which passes
over a communication-pulley p, falls between the
two tubes as the mercury rises in the branch bm^
and shows upon a graduated scale the variations
that occur in the level of the mercury in the dif-
ferent experiments. Supposing the length of the
instrument from M to 6 be 6^ feet, or 78 inches,
the ascending column may, if necessary, contain
1 56 inches of mercury ; and as a column of 1 56
inches of mercury with a basis of 1 square inch
weighs about 80 lbs., such a column may serve to
measure an effective pressure amounting to 809>8.
per square inch.
To graduate the scale of the instrument, we may
begin by marking first the point zero. For this,
the mercury and the water being poured in, as said
above, the two branches must be left to communi-
OF THE PRESSURE. 95
cate freely with the atmosphere, and the point
where the index stops will be the point sought, for
that is the position which the float naturally takes
when the branch Mb bears no more than the atmo-
spheric pressure.
The other extreme point of the scale must after-
wards be marked. Let ir be the pressure we want
to equilibrate; supposing the equilibrium established,
let X be the height at which, by virtue of that same
pressure tt, the mercury will stand above its natural
level in the branch m. The mercury having risen
in the branch m to the height x, it must have fallen
by an equal quantity in the other branch ; for the
mercury added on the one side can only proceed
from what has been taken off on the other. The
mercury in the branch M will therefore at the same
time be at the point /, and the whole part of that
branch, from the point x' to the point M, will be
filled by the water from the reservoir. If through
the point x' we draw an horizontal plane, the mer-
cury which is under that plane will equilibrate itself
in the two branches ; we have therefore nothing to
do with it, and need only consider the conditions of
equiUbrium for those parts which are above the
plane in the two branches. Now, we have on the
one side the pressure w, plus the weight of a column
of water in height Ma7'= 07; and on the other side,
we have a column of mercury in height 2x, plus the
weight of the atmosphere. P being the weight of
the column of mercury, F that of the column of
96 CHAPTER III.
water, and p that of the atmosphere, we shall have,
smce there is an equilibrium,
(w— p), which is the surplus of the real pressure of
the steam over the atmospheric pressure, is called
the effective pressure; and in all high-pressure
steam engines it is this which is to be considered.
The column of mercury, the weight of which we
have expressed by P, having for its basis the basis
of the tube which we shall express by 6, and for its
height the height^ 2a:, its volume will be 2bx; S
representing the density of the mercury, 2Sbx will
be the mass of the same column ; and g expressing
the accelerating force of gravitation, 2gSbx will be
its weight : that is to say, we shall have
P = 2gSbx.
By the same reason, S" being the density of the
water, the weight F of the column of water will be
expressed by gS^bx, its basis being also 6, and its
height Mx'=x. But the density of the water being
expressed by 1 , that of the mercury is expressed by
13- 568 ; thus we have
^'^ 13^568'
and consequently
^ ~ 13-568
On the other side, the effective pressure (w— p),
in whatever manner it be expressed, may be replaced
OF THE PRESSURE. 97
by the weight of a column of mercury, that would
produce the same pressure on the basis b. If then
h be the height of that column, which it is easy to
calculate, we shall have
ir '^ p=^ gSbh ;
and the equation of equilibrium will thus be
gSbx
2gSbx = jg.ggg +gcbh,
which gives
13-568
a? = A X 26l36 ~ AxO-51913.
The height A of a column of mercury, which may
represent a given pressure, is easily found ; for we
know that a column of mercury, one inch high,
presses on its basis at the rate of 0*4948 lb. per
square inch. The height of any other column may
thus be proportionably calculated. Wishing, for
instance, to represent a pressure of 70 lbs., we have
70 in.
h= 0:4043 X 1 = 141-47 inches;
so that, by this value of A, the quantity sought x
will be
X = 141 -47 in. X 0-51913 = 7344 in. ;
that is to say, that to correspond to an effective
pressure of 70 lbs., the height of the mercury must
be 6 feet 1^ inches.
The same calculation is applicable to any inter-
mediate point that may be sought, but it would be
H
98 CHAPTER III.
unnecessary trouble; for, knowing the point cor-
responding to zero, and that which corresponds to
the maximum pressure of the instrument, we have
only to divide the interval into equal parts, and the
scale will be suitably graduated, having seen that
the geiferal value of x depends solely on the cor-
responding value of hy and is proportional to it.
When the pressure to be measured is but slight,
as the apparatus need not then be of very great
height, a manometer on the above principle may be
fixed on the engine. Thus in the experiments on
the pressure caused by the blast*pipe, which we shall
report hereafter, we made use of a smaU manometer
of this kind constructed by Mr. E. Woods, engineer
to the Manchester and Liverpool Railway Company,
and found it act commodiously and surely. It was
capable of marking pressures amounting to 8fi>s.
per square inch. But to prevent the mercury from
being driven out all at once in the sudden changes
of pressure, or from making too great oscillations
during the motion, recourse had been had to the
known means of lessening the tube at the junction
of the two branches of the syphon. This disposi-
tion had no other inconvenience than that of sUghtly
diminishing the sensitiveness of the instrument.
The barometer-gauge which has just been de-
scribed is not portative, in the case, at least» when
it is required to measure high pressures. It must
remain fixed to the wall where it has been once
set up, and cannot accompany the engines in their
OF THE PRESSURE. 99
journey. If, the valve being once regulated, the
^igines preserved a constant pressure throughout
their motion, this objection would be unimportant,
and the instrument alone would satisfy all the
wants. The valve being fixed at the intended
wDridng point, the corresponding pressure would
be determined once for all, and provided no change
were made at the spring of the valve, the pressure
of the engine would be known at every moment of
its work.
But this is not the case. Nothing is more vari-
able than the pressure of the steam during the
motion of the engines. When, for instance, the
valve has been regulated for 50 lbs. per square inch,
that is, so as to begin to give issue to the steam as
soon as the pressure shall arrive at that point, we
are not thence to conclude that the effective pres-
sure will never, during the motion of the engine,
be less than 50fi>s., nor that it will never be greater.
Both these states will occur without any change
being made at the valve. If the steam does not
cause the valve to blow, the only derivable con-
clusion is that the effective pressure is under 50 fi>s. ;
but in trying it then, either by loosening the spring
or by the gauge, it will be found varying every
moment according to the activity of the fire, the
play of the pump, the inclination of the road, and
many other circumstances apparently indifferent:
at times the pressure will be only 15 or 18 lbs.,
then it will rise to 40 or 50 lbs. On the contrary,
i
100 CHAPTER III.
if the steam is seen to blow at the valve, all that
can be affirmed is that the effective pressure is
above 50 lbs. But we must beware of believing,
as at first we might be tempted to do, that because
the valve rises as soon as the pressure reaches
50 lbs., it from that moment gives free vent to
the steam, and that therefore the pressure of the
latter can in no case rise above that point. Let
the engine in this state be submitted to the gauge,
and it will be seen that the pressure, instead of
being restricted to 50 lbs., may be 60 lbs., and even
more.
It will in effect be readily conceived that if a
great part of the steam of the boiler escapes by
the safety-valve, that steam can issue forth as fast
as it is generated, only by raising the valve very
high, in order to make for itself a sufficient passage.
But the valve, as it rises, presses more and more on
the spring. The latter then opposes a resistance by
so . much the greater ; and consequently, the steam
requires an elastic force by so much the greater, as
it needs to create for itself a larger issue. As,
moreover, the spring marks 50fts. only when the
valve begins to rise, it is plain that the more its
rising is increased, the more the corresponding
pressure of the steam will exceed 50 fts. per square
inch. .
The changes of pressure which we have just
mentioned take place during the motion of the
engines, that is to say, while they are separated from
OF THE PRESSURE. 101
the stationary gauge. The latter then can no longer
be used directly to give the pressure of the steam ;
but, combining it with the observation of the safety-
valve, a knowledge of the pressure may still be at-
tained. In order to effect this, the engine must first
be set at work, varying the starting point of the
valve as it may appear necessary in the experiment ;
but two things are to be carefully noted, viz., the
point at which the valve was fixed as the starting
point, and its subsequent rise above that point.
The experiment being ended, the engine must be
brought back to the stationary gauge ; then, fixing
the valve successively at the different starting points
which have beea taken, and producing, moreover,
by urging the fire, the divers elevations above those
points, which have been observed during the ex-
periment, the degrees of pressure to which they
correspond may be written off from the barometer-
gauge. Thus will then be formed, for each engine,
a register which will render it easy to pass from the
indications of the valve, during the work, to the
actual pressures of the steam in the engine.
This mode, which is very practicable, is that
which we employed when we had only the valve
and the barometer-gauge to measure the pressure of
the steam in locomotives ; but the portable instru-
ments, which we are about to describe, render this
proceeding unnecessary, and are, besides, far more
convenient.
102 CHAPTER III.
Sect. II. Of the Air-gauge,
The air-gauge is represented in fig. 17. This
instrument, long known, but recently applied to the
use of locomotives, consists of a tube sealed at the
top, in which a portion of air compressed indicates
by the more or less diminution of its volume, the
pressure exerted on it by the steam. This tube,
exhibited at 1 1, is terminated at the upper part by a
ball full of air, the object of which is to expose to
compression a greater volume of air, without how-
ever requiring too great a length of tube. The
tube, at the lower end, is terminated by another
ball 6, but this is filled with mercury, which rises
also to a certain height x in the tube.
Near the top of the lower ball is a capillary
aperture o, through which the steam can exercise a
pressure on the mercury. The smaUness of the
aperture prevents the mercury finom being easily
spilt on conveying the instrument from place to
place ; but it would be bett^ so to contrive as to
be able, on occasion, to close it by means of a cock.
In order that the lower ball may be put in contact
with the steam, and that the upper portion of the
instrument may still remain exposed to view, the
tube is fixed in a metallic case, divided into two
compartments by a horizontal partition CC; and
the tube in traversing this partition, to whidi,
moreover, it is hermetically sealed, has its lower
ball enclosed in the lower compartment of the case.
OF THE PRESSURE. 103
and its upper part, on the contrary, in the superior
compartment, which is opened through its whole
length hy a longitudinal groove aadd. The case
fixes, by means of a moveable nut, to a tap on the
boiler, and, on the turning of a cock, the steam
penetrates freely, by the aperture O, into the lower
compartment of the case. It consequently presses
on the surface of the mercury through the passage
0, and the mercury rises in the tube till the elas-
ticity of the compressed air, together with the
weight of the mercury raised in the tube, equili-
brate the pressure exerted by the steam. Divisions
marked on the edge of the longitudinal groove will
then indicate the corresponding pressures of the
steam.
The action of this instrument is founded on
Boyle's or Mariotte's principle already explained,
according to which the volume occupied by the air,
under the same temperature, varies in the inverse
ratio of the pressure which it sustains. It will
readily be seen, in consequence, how the divisions
of this instrument are established.
The capacity of the upper ball of the tube must
first be measured by taking the weight of the mer-
cury which precisely fills it, and measuring to what
length along the tube the same weight of mercury
would extend ; then the capacity of the ball may be
replaced, in the calculation, by an equivalent length
of the tube.
Afterwards, having introduced a certain quantity
104 CHAPTER III.
of mercury into the lower ball and into the tube,
note is to be taken of the point at which the mer-
cury stops when the instrument is exposed merely
to the air. This point is evidently that which
corresponds to a pressure equal to the atmospheric
pressure, that is, to a total pressure of 14*71 Eng-
lish pounds per square inch, or, in other words, to
the weight of a column of mercury 30 English
inches in height.
This premised, in order to know the point cor-
responding to any other pressure of the steam, let P
be that pressure in inches of mercury, and ir the at-
mospheric pressure similarly expressed ; let L also be
the total length of the tube from the orifice o to the
top, including in this measure the length of tube
which represents the capacity of the ball filled with
air, as has been explained above. Finally, let h be
the height of the level of the mercury in the tube
above the orifice o, when the instrument supports
no more than the atmospheric pressure, and H the
height of the same level, when the instrument is
submitted to the pressure P.
It has been said that the spaces occupied by the
compressed air are in the inverse ratio of the pres-
sures which they sustain. Now, when the instru-
ment is exposed to the atmospheric pressure tt,
since that pressure is then held in equiUbrio by
the resistance of the air contained in the tube,
plus the weight of the column of mercury whose
height is A, it is plain that the resistance of the
OF THE PRESSURE. 105
air, or the pressure which it sustains, is represented
by
w — A.
Similarly, the resistance of the compressed air,
under the external pressure P, is expressed by
P-H.
Finally, the spaces respectively occupied by the
compressed air, under the external pressures ir and
P, are L — A and L — H. We have therefore the
analogy
L-H- 9r-A^
whence is derived
L — A
P = H + (tt - A) jj3^-
Consequently, it will be easy, by means of this
equation, to know the pressure which corresponds
to a given division of the instrument; and after
having thus determined a sufficient series of pres- ,
sures, and inscribed them on a preparatory scale,
then by interpolation may readily be deduced there-
from, a definitive and regular scale, indicating the
elevations of the mercury for all the pressures
required.
The problem may equally be resolved in a direct
way, without any interpolation ; that is to say, the
elevation of the mercury corresponding to a deter-
mined pressure^ may be found immediately ; for the
same equation, resolved above with reference to the
106 CHAPTER III.
pressure P, may also be resolved with reference to
H. It then gives
L+P
H=-^-i ^(L-P)^ + 4(7r-A) (L-A),
which expresses the elevation sought. It is how-
ever to be observed, that this equation is susceptible
of another solution, in which the radical would be
affected with the sign plus instead of minus. But
the second solution, though it would satisfy the
definitive equation of the calculation, does not apply
to the question proposed ; for, in the case of P = w,
the equation must give H = A, and consequently the
radical must be affected with the sign minus^ as it is
easy to verify.
The value of H thus found makes known imme-
diately the point of the scale which corresponds
to a determined pressure P, but as that value re-
quires a calculation somewhat complicate, the former
method will no doubt be preferred in practice. In
either solution, the pressure of the steam is always
expressed by the height of an equivalent column of
mercury. Thus in the first solution, the result once
obtained will have to be converted into pounds per
square inch ; and in the second solution, it will be
requisite previously to convert the given pressures,
from their usual expression, into an equivalent one
in inches of mercury. But these mutations present
DO difficulty, since it is known that a pressinre of
14-7 1 lbs. per square inch is equivalent to a column
of mercury of 30 inches in height.
OF THE PRESSURE. 107
From what has been said then, the divisions of
the instrument may be marked for every point of
the scale of pressures. It is however to be observed,
that Mariotte's law, on which the preceding calcula-
tion is founded, is exact only so long as the air
retains the same temperature in the different states
of €x>mpression. In order that the divisions thus
marked should be strictly accurate, the upper part
of the instrument, that is, the portion filled with
air, should always remain at the temperature of the
external air. This result is obtained to a certain
degree, even when the pressure, and consequently
the temperatm^ of the steam, become very consi-
derable, because the upper part of the case Ues open
as much as possible to the contact of the air, and
in the rapid motion of a locomotive, the contact
of the external air incessantly renewed, tends to
destroy all increase of temperature that might be
transmitted from the steam to the air compressed in
the tube.
In ordinary cases, then, the above-mentioned
consideration may be dispensed with. It is clear
however that this cause of error may easily be
avoided, by adopting another proceeding to effect
the graduation of the instrument. There may be
attached first to the tube a provisional scale, divided
merdy into very small portions, and the instrument
thus prepared may be put on a boiler in communi-
cation with a fixed barometer-gauge. Then as the
barometer-gauge shall be seen to denote pressures
i
108 CHAPTER III.
more and more elevated, the corresponding divisions
of the provisional scale of the air-gauge may be ob-
served, and consequently there will thus be formed
a register from which the definitive scale of the
instrument must afterwards be made out.
Albeit, if this mode have not been used to effect
the primitive graduation of the instrument, it is that
at least which ought to be used to verify that gradu-
ation, if the certainty of its accuracy be desired ; and
it is what we have always done before employing the
air-gauge in our experiments. Moreover, it is plain
that when the instrument is exposed to the external
air, the mercury ought, save the slight modifications
that may have occurred in the barometrical pressure
of the atmosphere, to rise in the tube to the point
marked for the atmospheric pressure, that is to say,
to the effective pressure zero. This is then another
verification not to be neglected, when recourse is
not to be had to the preceding.
The air-gauge is portative and very commodious.
It is usually not more than 10 inches long by an
inch in thickness, and may be affixed with ease to
all engines. But the divisions of the scale must be
marked with the greatest accuracy, which presents
some difficulty. The air too contained in the tube
must be thoroughly free from all humidity, for that
would become steam at the moment of the experi-
ment. In fine, a drop of mercury lost in carrying
the instrument, or a small quantity of water insinu-
ated by means of the steam, into the lower ball,
OF THE PRESSURE. 109
may falsify the divisions. It is only then on being
assured that the instrument is put out of hand by a
careful workman, and as far as it may be possible,
OD having proved it by the barometer-gauge, that
entire confidence is to be had in its indications.
Sect. III. Of the Thermometer-gauge.
The thermometer-gauge is an instrument as simple
and as portative as the preceding ; it is contained in
a case similar to that of the air-gauge, and is simi-
larly attached to the boiler by means of a moveable
nut. This instrument, represented figure 19, is
merely a thermometer, the ball of which is im-
mersed in the boiler, and whose upper part rises
above to expose to view the height to which the
mercury rises.
To establish this instrument, it evidently suffices
to take an ordinary thermometer and to replace the
degrees of temperature by the corresponding degrees
of pressure, in steam in contact with the liquid,
according to the Table which we have given in the
preceding chapter of this work. In order however
that the degrees thus marked should be quite exact,
it would be necessary to protect the ball of the ther-
mometer against the compression which the elastic
force of the steam tends to exercise on it, by a
double casing, and that double casing would destroy
all the sensitiveness of the instrument. In high
pressures, the degrees of pressure indicated by the
scale will be found then liable to a certain inaccu-
110 CHAPTER III.
racy, unless, besides replacing the temperatures by
their corresponding pressures, as has just been indi-
cated, the latter be also corrected by taking account
of the compression of the ball of the tube. In order
to effect this, it will suffice to set up the instrument
on an engine put in communication with a stationary
barometer-gauge, and to observe, by the comparison
of the two instruments, what correction ought to be
made in the principal points of the scale. In this
way will be avoided the causes of error that have
been pointed out, and consequently the instrument
can be verified when any doubt is entertained of its
accuracy. We have invariably availed ourselves of
it before using the instrument in our experiments.
The thermometer-gauge is both portative and
commodious, but it wants accuracy when the
pressure of the steam suffers rapid changes, which
is constantly happening with locomotive engines :
the time requisite for the instrument either to
wann or to cool to the temperature of the steam,
will not then allow it to indicate the pressure cor-
rectly. Another inconvenience still more serious is
that, for high pressures, which are precisely those
most generally wanted, the divisions are exceedingly
small because the corresponding variations of tem-
perature are very trifling. The instrument then be-
comes unsure, and, in the rapid motion of the en-
gine, almost illegible, unless its dimensions, which
are usually about 10 inches in length, were enlarged,
and the instrument made less commodious on that
account.
OF THE PRESSURE. Ill
Sect. IV. Of the Spring-gauge or Indicator.
The above-mentioned defects of each of the pre-
ceding steam*gauges induce us to recommend try-
ing, for locomotives, the use of the indicator of
Mr. Watt, the construction of which properly fells
into the department of engine manufacturers, where-
as the other gauges require the aid of the optician.
This instrument is represented figure 23. It
consists of a small brass cylinder, similar to the
case of the two preceding gauges, and, like them,
fixed temporarily to the boiler. Its lower part
contains a piston P, susceptible of rising and fall-
ing in the cylinder, and admitting the steam to
act imder it. The area of the piston ought to be
precisely one square inch. On its upper part is a
rod ^ which is maintained by a ring cc, in the
exact direction of the axis of the cylinder. This
rod acts against a spiral spring SS, similar to those
of the ordinary spring-balances, and presses it with
more or less force according as the piston is more or
less raised by the action of the steam. A longi-
tudinal groove aahh is made on the upper part of
the instrument, so that an index t, moving with the
head of the spring, juts out fi:om the groove, and
by means of a scale engraved on the edge, indi-
cates the pressure sustained by the spring, and con-
sequently the effective pressure of the steam under
the piston, that is, in the boiler.
In order to divide the instrument, it suffices to
112 CHAPTER III.
withdraw the piston and ascertain its precise weight.
It must then be put back into its place, the cylinder
reversed, and the piston loaded at first with a
weight of 1ft., diminished by the weight of the
piston itself. The point at which, under this
weight, the index rests is marked 1 ft. ; then add-
ing successively other weights of 1ft., 2fts., &c.,
the respective points at which the index stops will
be marked. This operation once finished, it is
plain that when the steam shall have an elastic
force of 1ft., 2fts., &c. per square inch, it will
make the index rise to the corresponding points
of the scale ; and the precaution of having in-
cluded the weight of the piston in that of the
first pound applied on the spring, causes the weight
of that piston to come naturally into account in all
cases as it ought to do. Thus the instrument will
give immediately the pressure per square inch in
the boiler.
The verification visibly reduces itself to measuring
the diameter of the cylinder and placing anew some
weights on the piston, to ascertain that the divisions
of the scale are exact, that the friction of the piston
has not varied, and that the spring has presehred its
proper elasticity. That the piston may have pre-
cisely a square inch of surface, its diameter ought
to be ri283 inch, or 1 inch ^ and a fortieth of an
eighth. The omission of this latter fraction, that
is, the use of a piston 1^ inch in diameter, would
only cause an error of -^hj of a pound minus, which
OF THE PRESSURE.
113
would make a quarter of a pound on an effective
pressure of 50 lbs. per square inch.
Sect. V. Comparative Table of the divers modes of
expressing the pressure.
As the pressure of the steam is expressed in several
ways, and as in this work we use but one, we here
subjoin a Table of correspondence of the divers
modes of expressing it.
Comparative Table of the different modes of expressing the
pressure of the steam.
Excess of that
force above the
atmospheric pres-
ToUl
or ibsolttte pressure of the steam |
sure, or pressure
called effectwe
in high-pressore
engines,
in lbs. per
in lbs. per
in
inch
inch
in inches of
in lbs. per
atmospheres.
square.
circular.
mercury.
square inch.
1
14-71
11-55
29-92
*f
1-5
2206
17-33
44-88
7-35
2
29-41
23- 10
59-84
14-71
2-5
36-77
28-88
74-80
2206
3
44-12
34-65
89-76
29-41
3-5
51-47
40-43
104-72
36-77
4
58-82
46-20
119*68
44-12
4-5
66-18
51-98
134-64
51-47
5
73-53
57-75
149-60
58-82
5-5
80-88
63-53
164-56
66-18
6
88-24
69-30
179-52
73-53
6-5
95-59
75-08
194-48
80-88
7
102-94
80-85
209-44
88-24
7-5
1 10-30
86-53
224*40
95-59
s
117-65
92-40
239-36
102-94
CHAPTER IV.
OF THE RESISTANCE OF THE AIR.
Sect. I. Of the intensity of that resistance on the
unit of surface.
Thb resistance of the air against the waggons
cannot be regarded as a force to be neglected in
calculations relative to motion on railways; for it
is well known that trains, left to themselves, have
at times been dragged to considerable distances by
the mere impulse of the wind, and that engines in
full course have literally been brought to a stand-
still by momentary gusts of wind contrary to their
direction.
It is necessary then to take into account the effects
of the resistance of the air against the trains. The
exact evaluation however of that resistance offers
some difficulty. Borda's experiments,^ as well as
those of Rouse and Edgeworth,^ prove that the
resistance of the air, within the limits which we
have to consider, increases in the ratio of the square
of the velocity ; and so far they are decisive : but
^ M^moires de TAcad^tnie des Sciences, ann^ 1763.
^ Philosophical Transactions, 1 782.
RESISTANCE OF THE AIR. 115
as to the absolute yalue of the resistance of the air,
it cannot satisfactorily be determined by these ex-
periments, because on larger surfaces being put to
trial, there resulted resistances greater per unit of
surface, leaving thus a doubt as to the choice to be
made between these different results.
Nevertheless, till very lately, the only mode of
estimating the resistance of the air was by the
determinations of Borda. A work, but little known
as yet, that of M. Thibault,^ has however appeared,
and furnished much more precise data on the sub-
ject.
Borda's experiments had been made in a circular
motion, and Dubuat ^ had already thought that the
singular anomaly which they presented, to wit, that
of resistances increasing in a greater ratio than the
surfaces, must proceed from the nature of the cir-
cular motion itself. He had in fact observed, that
a body set in motion in a fluid always draws a
portion of the fluid after it, and that this portion
of fluid, attached to the moving object, is inces-
santly disturbed and driven back by the molecules
of fluid which, after having sustained the shock of
the moving surface, escape around its edges and
rush behind it. There will always then be pro-
duced a partial vacuum, or diminution of pressure.
^ Experiences but la resistance de Fair, par M. Thibault, lieu-
tenant de Vaisseau, Brest.
* Principes d'Hydraulique.
116 CHAPTER IV.
or, as Dubuat has termed it, a non-pressure^ behind
the moving body; and as the definitive resistance
against that body, is nothing else but the difference
of the pressures exerted by the air against the
front and hind surfaces, it follows that the re-
sistance of the air against a moving body will always
be increased, whenever the diminution of pressure
behind the body shall become more considerable.
Now if we suppose a surface of a given magnitude,
set in motion in a straight line, there will be caused
behind it a non-pressure, and the resistance suffered
by the moving body will be the difference between
the pressure of the air in front and the diminished
pressure which subsists behind. If, after this, the
body be submitted to a circular motion, it is evident
that in proportion to the greater curvature of the
Une described by the body, the air, after passing over
its edges, wiU by so much the more disturb the portion
of fluid which follows it, and thus the pressure be-
hind will be diminished; whence will result a greater
resistance against the moving body. Again, if the
latter be brought nearer the centre of motion, this
same effect will be augmented. Definitively then,
the resistance against a given surface, in a circular
motion, will become greater as the surface is nearer
to the centre of rotation ; and in order that two
surfaces of different magnitudes have to contend
with an equal degree of disadvantage, — in other
words, that the resistance of the air, per imit of
surface, be the same for each, — those two surfaces
RESISTANCE OF THE AIR. 117
must be placed at distances from the axis, propor-
tional to the sides of the squares which represent
them.
This in effect has been verified by the experi-
ments of M. Thibault^ which have demonstrated,
that in a circular motion, the apparent augment-
ation of the resistance of the air against large
surfaces, compared with smaller ones, arises merely
from the fact of their not being removed to a dis-
tance from the axis, proportional to the length of
their side ; that, subjected to this condition, the
large surfaces, as well as the small, experience resist-
ances really proportional to their extent ; and that
when non-subjected to this condition, the greater
surfaces, on the contrary, may have to overcome
resistances, per imit of surface, double those op-
posed to the surfaces of smaller extent. It is then
to be concluded from those experiments that the
circular motion cannot, with any accuracy, be used
in determining the resistance of the air in a direct
motion, unless the surfaces employed be of very
small extent compared to the length of the radius
of rotation.
The experiments of the same author confirm,
moreover, two results already obtained by Dubuat
with respect to liquids, and indicated by him with
respect to fluids. The first of these results is,
that the resistance against a body moving in an
indefinite fluid, at rest, is less than the resistance
experienced by the same body placed at rest in an
118 CHAPTER IV.
indefinite fluid moving against it, which seems to
denote that a fluid in motion separates itself less
easily than a fluid at rest. The second is, that a
thin plate meets with a greater resistance from the
air than a prismatic body presenting in front the
same surface, and that the resistance diminishes
according as the prism is longer. This circum-
stance is occasioned thus : the air having glided
over the edges of a thin body, rushes immediately
behind it with great rapidity, and carrying in its
motion the portion of fluid, which we have men-
tioned above, produces a relative vacuum behind
the opposed surface. But if the moving body be a
lengthened prism, the air in passing along its sides
loses a certain portion of its acquired velocity, and
consequently, on reaching the hind face of the
prism, extends itself behind it with a force more
and more moderated ; whence results that it pro-
duces there a partial vacuum, or non-pressure, less
considerable than in the case of a simple sur&ce.
And as we have seen that the definitive resistance
against a moving body is the difierence between the
pressure of the air in front and the partial vacuum
created behind, it follows that longer bodies de-
finitively suffer from the air a less resistance than
bodies of inconsiderable thickness.
Besides, the experiments of M. Thibault have
confirmed those of Borda, on the proportionality of
the resistance of the air to the square of the ve-
locity, within the limits of velocity that we have
RESISTANCE OF THE AIR. 119
to consider in this work. They have, moreover,
demonstrated that if two square surfaces be placed
so that one shall precisely screen the other, and at
a distance apart equal to one of their sides, the
resistance against the screened surface will be
7-tenths of the resistance suffered by the surface in
front. It consequently results that, when two sur-
faces are separated by a considerable space relatively
to their extent, the resistance of the air against the
second is to be estimated nearly as if it were iso-
lated in the air; but if, on the contrary, the two
surfaces are very near each other, relatively to their
extent, there is room to think that the screened
surface may be almost entirely protected against the
effect of the air, since a space equal to one side of
the surface would be requisite for the air to exert
against it a resistance equal to two-thirds of the re-
sistance against an isolated surface.
Finally, uniting the results obtained by Borda,
Dubuat, and M. Thibault, and limiting ourselves to
the case of a body moving in the air at rest, which
is the only case that occurs in this work, we have,
to determine the resistance of the air, the following
formulae, in which S represents the front surface of
a body traversing the air in a direction perpen-
dicular to that surface, V the velocity of the motion,
e a co-efficient variable with the length of the body,
and, lastly, Q the definitive resistance produced by
the air against the body.
120 CHAPTER IV.
Q= 0011896 € ^ V^ . . Resistance of the air ex-
pressed in English fts.,
the surface S being ex-
pressed in square feet,
and the velocity V in
English feet per second.
And in applying these formulae it will be necessary,
according to the case, to give to the letter e the
following values :
for a thin surface 6= 1*43
for a cube e=ri7
for a prism of a length equal to
three times the side of its
front surface 6=1 '10
Sect. II. Of the resistance of the air against the
waggonSy isolated or united in trdins.
From what we have just seen, it will be easy to
estimate the resistance of the air against a prismatic
body in motion, when its front surface and dimension
in length are known. But as a waggon does not
present a regular prismatic form, it becomes neces-
sary first to consider how we may find what surface
it really offers to the shock of the air.
The front surface of a waggon may be directly
measured; it consists of two distinct parts, the
surface of the load and that of the waggon itself.
RESISTANCE OP THE AIR. 121
The former of these surfaces necessarily varies
according to the nature of the goods which form
the load; and as to the surface of the waggon,
properly so called, on railroads of 4 feet 8^ inches
width of way, and for waggons with a single plat-
form, it usually amounts to 14'33 square feet. But
this is evidently not the only surface against which
the air exerts its resistance ; for the spokes of the
wheels cannot turn rapidly as they do, during the
motion, without meeting with a certain resistance
from the air ; and again the axle-trees, axle-boxes,
springs, and hind-wheels of the waggon, are sepa-
rated far enough from the similar pieces which
precede them, not to be considered as wholly pro-
tected against the shock of the air.
Considering separately a wheel of 3 feet in diameter,
like that of the ordinary waggons, and reducing the
surface of all its spokes, whose divers points have dif-
ferent velocities according to their distance from the
centre, to the surface which, being moved at the ve-
locity of the circumference of the wheel, would suffer
from the air an equivalent resistance, each wheel is
found to offer in this respect a surface of 1 *25 square
feet. Adding then the direct surface offered by the
nm of the wheel seen in front, as well as by the naves,
axles, and springs, we arrive at this result, that each
pair of wheels presents to the shock of the air a
total surface of 7*03 square feet. Now, if we con-
sider, either in an isolated waggon or in a train
composed of several waggons, every pair of wheels
122 CHAPTER IV.
except the first, we shall observe that all present
that extent of surface to the shock of the air ; but
as the whole of that surface is screened, to wit, the
spokes by those which precede them in the motion,
and the wheels, naves, and axles, by the similar
pieces in the pair of wheels preceding them, we
shall approximatively take this circumstance into
account by assimilating the effects of the air on
these successive pieces, to those observed by M.
Thibault in the case of surfaces screened by each
other and separated by an interval equal to the side
of their square, which is not far from the truth in
the case under consideration. We shall then reduce
the above surface to two-thirds, and shall -thus have
4*69 square feet, for the direct surface opposed to
the shock of the air during the motion of the
waggons, by each pair of wheels exclusive of the
first.
Now, as to the fore- wheels of the first waggon,
the surface of projection of the rims, springs, &c., is
already reckoned in the total front surface of the
waggon, but account must also be taken of the
rotation of the spokes, which for this pair of wheels
reduces the number 4*69 to 1*67 square feet. It
follows then firstly that, for an isolated waggon, the
addition to be made to its front surface, or rather to
its surface of projection directly measured, for the
fore and hind-wheels, should be 6 square feet. Fur-
thermore, for the same case, as a loaded waggon
presents, at a medium, a length equal to once and a
RESISTANCE OF THE AIR. 123
half the square root of its front surface, we should
in the preceding formulae make 6 = 1*15.
As to the trains of several waggons, we at first
see that, for the resistance of the wheels, an addition
must be made to the transverse section of the train,
of 9 square feet per intermediary waggon and of 6
square feet only for the first ; but as the waggons
composing the same train, though very near each
other, are not however in contact, it is necessary
further to seek upon what extent of surface, these
waggons thus united still suffer the resistance of the
air during their motion.
In order to effect this, we operated in the following
manner :
On the 3rd of August, 1836, accompanied by
Mr. E. Woods, engineer of the Liverpool and Man-
chester Railway, we took five waggons, of different
heights, loaded with goods, and measured their
front surfaces. These waggons were then drawn
to the incUned plane of Whiston, an exact section
of which will be given in the following chapter.
They were then abandoned, separately, to their own
gravity, and as the inclination of the plane was suf-
ficient to decide their motion, they ran down of
themselves, and having passed the foot of the plane,
continued their motion along another plane much
less inclined than the former, till they were brought
to rest by the retarding forces, namely, the friction
proper to the waggons themselves and the resistance
of the air against their surface. After the waggons
124 CHAPTER IV.
had been submitted separately to this experiment,
they were brought back on the inclined plane to
the point from which they had first started, and
again abandoned to gravity, but all united in one
train.
As the friction proper to the waggons had evi-
dently not varied, it is clear that if the latter
experiment gave a total resistance greater than the
sum of the frictions of the five separate waggons,
augmented by the resistance of the air against the
transverse section of the train, the surplus must be
attributed to the indirect shock of the air against
the successive surfaces of the intermediary waggons
of the train ; and, consequently, a valuation of that
efiect was to be obtained.
We shall explain, in the following chapter, in
what manner the friction of the waggons was
concluded from the circumstances of their motion
on the two inclined planes ; in this place it will
suffice to relate the results of six experiments, made
with a special view to determine the resistance of
the air against the intermediary waggons. In the
following Table, which contains these results, we
give, for the first five experiments, the weight of
each waggon and the surface it opposes to the
shock of the air, including the wheels and accessory
pieces, as has been indicated above.'^ In experi-
* When these experiments were published for the first time, an
error had slipped into the measm'e of the front surface of the
frame- work of the waggons ; which error is corrected here.
RESISTANCE OF THE AIR. 125
ment VI., made on the waggons united, the surface
carried into the eighth column is successively : first,
that of the highest waggon of the train, augmented
by the surface representing the resistance of the
wheels and the screened parts ; and, afterwards, the
surface which gives, for the five waggons together,
a friction equal to the sum of the frictions of the
five waggons separate. The other columns make
known the circumstances of the experiment, and
consequently determine the friction of the waggons,
as will be seen in the following chapter. To cal-
culate the resistance of the air, we have taken in
the case of the separate waggons €=1'15, as has
been said above ; and for the case of the connected
waggons, as they formed a prism of a length equal
to seven times its width, we have taken, according
to the observations of Dubuat, 6= 1*07.
During these experiments the weather was fine, a
slight air was perceptible in the contrary direction
of the motion, but its action was so weak that a
wind-gauge, exposed in an open place, could give
no appreciable valuation of it.
As to the mode of experiment here employed, we
must say, that when the resistance of the air against
the front surface of the trains only is considered, it
may appear that during the descent of the five
waggons united, they must have pressed strongly
one against the other, because the shock of the air,
which was the resistance, exerted its effort against
the front, whereas the gravity, which was the mo-
126 CHAPTER IV.
tive force, acted nearly in the centre of the mass in
motion. Hence, therefore, it might be concluded,
that this pressure of the waggons one against the
other would throw them out of square upon the
line, and consequently, in this case, make their
friction appear greater than it really was. But it
must be observed, that in experiment VI. the wag-
gon of greatest section was put last in the train,
and again, that the resistance of the air exerted
itself against each mtermediate waggon, which di-
vided that resistance over the different points of the
train, instead of concentrating it on the front sur-
face. Moreover, a pressure of the wagons one
against the other may, in effect, throw them out of
square when they are connected by stiff bars, be-
cause the shortening of the train then tends to set
those bars across, and thus drive the wagons against
the rails on either side. But the waggons here em-
ployed were not of this kind; they were joined
together merely by chains, and in that state the
mutual contact took place by the projecting ends of
the frame on each side; consequently, it could
only tend to maintain them more directly on the
road, since, in such a system of junction, the
shortest line the train can form, or that which is
determined by the pressure of the hinder waggons,
is not a crooked line as in the case of the stiff bars,
but a straight and direct line from one end of the
train to the other. None of these accessory effects
then occurred in the experiments which we are
about to report.
RESISTANCE OF THE AIR.
127
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128 CHAPTER IV.
From this Table it appears, that limiting our-
selves in experiment VI., to taking account of the
resistance produced by the rotation of the wheels
and by the screened pieces of the frame-work of
the waggons, the friction of the five waggons de-
duced from this experiment, seems to be more
considerable than the sum of the frictions of the
same five waggons, deduced from the preceding
experiments ; and that it is only by adding 3 square
feet more to the surface exposed to the shock of
the air in experiment VI., that we are enabled to
put the result of that experiment in harmony with
those of the separate waggons. We must then
conclude, that besides the resistance opposed by
the air against the wheels and the screened pieces
of the frame- work, there was still a surface of 3
square feet for the four waggons which followed
the first, or a surface of 1 square foot per waggon,
exposed to the shock of the air during the motion.
That is to say, the air after the passage of the
first waggon, rushed between that waggon and the
following one, and notwithstanding the small in-
terval which separated them, it still exerted on the
second waggon a certain action, the intensity of
which might be represented by the shock of the
air against 1 square foot of direct surface.
Consequently, adding this new surface to that
already obtained to represent the motion of the
wheels and accessory pieces, we see that when a
train of waggons is in motion on a railway, it is
RESISTANCE OF THE AIR. 129
necessary, in order to estimate the effects of the
resistance of the air against its progression, to take
as resisting surface that of the waggon of greatest
section, augmented by 10 square feet per interme-
diary waggon, and by 6 square feet for the first
waggon, including of course in this number the
engine itself and its tender.
On railways of about 5 feet width of way, the
surface of the highest waggon may at a medium be
reckoned at 70 to 74 square feet ; we may then
esteem, in general, the resisting surface of a train
of waggons at 70 square feet, plus as many times
10 feet as there are carriages in the train, including
the engine and its tender. If the train consists
of diligences, as their surface is from 60 to 64
square feet, then in the preceding estimation the
number 70 must be replaced by the number 60.
If the road has a wider way, or if the carriages
ofier a surface difibrent from that we have just
indicated, the carriage of greatest section must be
measured, and that measure used, instead of the
number 70 or the number 60 of the above calcu-
lation. If the wheels of the waggon are more than
3 feet in diameter, there will likewise be an addition
to make, to take account of the greater surface
which they expose to the shock of the air during
the motion. This addition would be about 3 square
feet per waggon, for wheels of 5 feet in diameter
instead of 3. Finally, if the interval between the
K
130 CHAPTER IV.
waggons, instead of being about 2 feet, as it was
in experiment VI., and as it is at a medium on
ordinary railways,^ considering the diflferent kinds
of carriages and the inequalities of their loading,
were augmented by any important quantity, there
might also be some addition to make for the effect
of the air against the loads of the successive
waggons ; but as our determination in this respect
gave something less than 1 square foot per waggon,
and as the interval between the waggons could not
be augmented by any thing considerable without
being liable to inconveniences in practice, we deem
that 1 square foot per waggon may comprehend
nearly all cases.
When the effective surface presented to the shock
of the air shall be known by the preceding calcula-
tion, it must be substituted for the letter S in the
formulae given above, putting at the same time for c,
its value suitably to the length of the prism formed
by the train of waggons. According to the vari-
ation of € observed by Dubuat for prisms of divers
proportions, it will be found that in the case of a
train of 5 waggons, we must make € = 107, and
that the case of a train of 25 waggons would require
e = l-04. In order then not to have to return
continually upon these considerations we will take
as a medium 6 = 1*05, which is suitable to a train
of 15 waggons, and expressing at the same time,
in the formula given above, the velocity in miles
RESISTANCE OF THE AIR. 131
per hour, we shall have, in fine, to express the
resistance of the air against a train of waggons in
motion, the following formula :
Q = 002687 S v^ . . . Resistance of the air, in
pounds, the effective sur-
face of the train or the
quantity S being expressed
in square feet, and the ve-
locity of the motion in
miles per hour.
Sect. III. Table of the resistance of the air against
the trains.
To dispense with all calculation relative to the
resistance of the air, we here subjoin a Table show-
ing its intensity, for all velocities from 5 to 50 miles
per hour, and for surfaces of from 10 to 100 square
feet. Were it required to perform the calculation
for a velocity not contained in the Table, it would
evidently suffice to seek the resistance corresponding
to half that velocity and to multiply the resistance
found by 4 ; or, on the contrary, to seek the re-
sistance corresponding to the double of the given
velocity, and to take a quarter of the result. So,
the resistance of the air against a surface of 100
square feet, at the velocity of 50 miles per hour, is
equal to four times the resistance of the air against
the same surface, at the velocity of 25 miles per
132 CHAPTER IV.
hour. As to surfaces greater than 100 square feet,
they must be decomposed into surfaces less than
100 feet, and then the Table will still give the
results required; for the resistance against a sur-
face of 120 square feet is evidently nothing more
than the sum of the resistances against one surface
of 100 square feet and one of 20 square feet.
By means of the Table in question will be obtained,
without calculation, the resistance of the air expressed
in pounds, for any velocity of the moving body ; but
it is to be observed, that the Table supposes the
atmosphere at perfect rest. If then there be a wind
of some intensity, favourable to the motion or con-
trary to it, account must be taken thereof. In order
to effect this, it will suffice to observe that if the wind
is favourable, the body will move through the air
only with a velocity equal to the differ^ice between
its own absolute velocity and that of the wind ; and
that if, on the contrary, the wind is opposed to the
motion, the effective velocity of the body through
the air will be equal to the sum of its own velocity
augmented by that of the wind. In this cai&e, then,
the velocity of the wind must first be measured, by
abandoning a light body^ to its action, and noting the
time in which it traverses a space previously mea-
sured on the ground ; or else an anemometer may
be used for the purpose. Then the velocity of the
wind must be subtracted from that of the train in
motion or added to it, according to the case ; and
that difference or that sum is the velocity to be
RESISTANCE OF THE AIR. 133
sought in the Table, or substituted in the formula,
to obtain the corresponding resistance against the
whole train.
If the wind, instead of being precisely contrary or
favourable to the motion, should exert its action in
an oblique direction, it would tend to displace all the
waggons laterally ; and consequently, from the coni-
cal form of the wheels, all those on the farther side
from the wind would turn on a larger diameter than
those on the side towards the wind. The resistance
produced will therefore be the same as that which
would take place on a curve on which the effect of
the centrifugal force were not corrected, and that
resistance would necessarily be very considerable;
but as we have made no experiment on this subject,
we shall not dwell on it any longer here.
134
CHAPTER IV.
Practical Table of the resistance of the air against the
trains.
Velocity of
motion, in
mUes per
Resistance
of the air,
in lbs. per
square foot
Resistance of the air, in pounds ; the effective
surface of the train, in square feet, being :
hour.
of surface.
20
30
40
50
tbs.
60
tbs.
70
tbs.
80
tbs.
90
lbs.
100
tbs.
miles.
lbs.
ibs.
tbs.
lbs.
5
•07
1
2
3
3
4
5
5
6
7
6
•10
2
3
4
5
6
7
8
9
10
7
•13
3
4
5
7
8
9
11
12
13
8
•17
3
5
7
9
10
12
14
15
17
9
•22
4
7
9
11
13
15
17
20
22
10
•27
5
8
11
13
16
19
22
24
27
11
•33
7
10
13
16
20
23
26
29
33
12
•39
8
12
15
19
23
27
31
35
39
13
•45
9
14
18
23
27
32
36
41
45
14
•53
11
16
21
26
32
37
42
47
53
15
•60
12
18
24
30
36
42
48
54
60
16
•69
14
21
28
34
41
48
55
62
69
17
•78
16
23
31
39
47
54
62
70
78
18
•87
17
26
35
44
52
61
70
78
87
19
•97
19
29
39
49
58
68 1 78
87
97
20
1-07
22
32
43
54
65
75,' 86
97
107
21
1-19
24
36
47
59
71
83
95
107
119
22
130
26
39
52
65
78
91
104
117
130
23
1-42
28
43
67
71
85
100
114
128
142
24
1-55
31
47
62
78
93
109
124
140
155
25
1-68
34
50
67
84
101
118
134
151
168
26
1^82
36
55
73
91
109
127
146
164
182
27
1^96
39
59
78
98
118
137
157
176
196
28
211
42
63
84
106
127
148
169
190
211
29
2-26
45
68
90
113
136
158
181
203
226
30
242
48
73
97
121
145
169
194
218
242
31
2-58
52
77
103
129
155
181
206
232
258
32
2-75
55
83
110
138
165
193
220
248
275
33
2-93
59
88
117
147
176
205
234
264
293
34
3-11
62
93
124
156
187
218
249
280
311
35
3-29
66
99
132
165
197
230
263
296
329
36
3-48
70
104
139
174
209
244
278
313
348
37
3^68
74
110
147
184
221
258
294
331
368
38
3-88
78
116
155
194
233
272
310
349
388
39
4^09
82
123
164
205
245
287
327
368
409
40
4^30
86
129
172
215
258
301
344
387
430
41
4-52
90
136
181
226
271
316
362
407
452
42
4-74
95
142
190
237
284
332
379
427
474
43
4-97
99
149
199
249
298
348
398
447
497
44
6-20
104
156
208
260
312
364
416
468
520
45
5-44
109
163
218
272
326
381
435
489
544
46
569
114
171
228
285
341
398
455
512
569
47
5-94
119
178
238
297
356
416
475
535
594
48
619
124
186
248
310
371
433
495
557
619
49
6-45
129
194
258
323
387
452
516
581 645
50
6-72
134
202
269
336
403 470
1
538
605 672
1
CHAPTER V.
OF THE FRICTION OF THE WAGGONS ON
RAILWAYS.
Sect. I. Necessity of new inquiries on this subject.
From the description we have given of the engine,
it has been seen that the steam, acting on the
pistons, communicates to the wheels a rotatory
motion, which must infaUibly propel the engine,
provided the train which follows it do not oppose
a resistance greater than the force it commands.
An important inquiry then, as to the motion of
locomotives, consists in determining the resistance
caused by the trains which they have to draw.
These trains are formed of a number more or less
considerable of carriages called waggons, which are
loaded with goods. Their resistance to the motion
depends not only on their weight, but on the state
of the railway and on the more or less perfect con-
struction of the carriages. The object -in view in
the making of a railway being to produce a road per*
fectly hard and smooth, on which the carriages shall
roll easily, if the railway happen to be indifferently
maintained or otherwise to deviate from the con-
ditions for which it has been estabUshed, it is plain
136 CHAPTER V.
that the resistance opposed by the train along the
rails will be by so much the greater. The same will
occur if the carriages, from defective construction or
want of repair, have a considerable friction.
This observation shows that the force necessary
to move a given weight, a ton for instance, may not
be always the same, either on all railways, or with
all kinds of carriages. On rails perfectly even, and
with waggons well constructed and well greased, the
draught of a ton may require a force of but 6 fts.
We mean that a weight of 6fts. suspended by a
cord over a pulley, would suffice in this case to
move, or at least to maintain in motion, a carriage
weighing a ton. On another railway, on the con-
trary, and with carriages of a different construction,
the same load of a ton may require a much greater
force.
The old waggons on which some experiments had
been made, were supposed to require a force of
10 or 12 lbs. for each ton of weight of the load.
They had afterwards been improved, but had not
been submitted to any experiment made on a large
scale and in the regular working state. On the first
introduction of the new waggons, an essay was
indeed made on a single one and at the moment it
left the workmen's hands. But as this waggon had
been carefuUy oiled expressly for the trial ; as it had
as yet received no shock to bend the axle-trees, or to
throw the wheels out of square ; as the wheels were
new and perfectly round ; as, in fine, the rails had
FRICTION OF THB WAGGONS. 137
been carefully swept for the purpose, the result
of such an experiment could hardly be considered
as a practical result. So, on the Liverpool Railway,
the friction of the trains was still valued at lOfts.
per ton.
These uncertain data could not suit a new work,
or calculations made on modern waggons ; and
therefore we undertook, in order to determine the
friction of waggons, the series of experiments which
we are about to relate.
Sbct. II. Of the friction of waggons determined by
the dynamometer.
The most natural means of attaining the determi-
nation of the friction or resistance of the waggons
seemed to be to employ the dynamometer, since it
gives immediately the force of traction necessary to
effect the motion ; but, as the action of drawing,
whether by men, or any other animated mover, is
performed by pulls, the dynamometer merely oscil-
lates between limits wide apart, and can give no
certain result. It appeared to us, however, that if
the traction were performed by an engine whose
strain is always equal, and whose motion too is
regulated by the mass of the train itself, the
dynamometer would, perhaps, have but slight os-
cillations, and that the pulsations of the engine
would be insensible, especially on the hinder car-
riages.
138 CHAPTER V.
For this reason, at the moment the engine Leeds
started with a train of twelve waggons, when the
whole mass was set in motion, and that motion
continued at the uniform velocity of about three or
four miles per hour, the drawing chain of the last
three waggons was detached and replaced by a cir-
cular spring-balance, previously disposed for the
purpose. The rod of the balance was fixed to the
hinder part of the ninth waggon, and the three
following ones, which were the last of the train,
were fastened to the spring. The experiment took
place on the half mile from 1 ^ to 2 of the Liverpool
and Manchester Railway, on a space which is exactly
level.
We expected to see the balance nearly invariable ;
we were, however, deceived. The style maintained
itself most frequently about the point marking
100 lbs., but it was continually subject to great
variations, which went from 50 lbs., the least, to
170fts., the greatest; and even, in a sort of ex-
traordinary pull, which the engine gave at times,
the needle was seen to fly to the end of the balance,
which indicated 220 lbs. The latter case, however,
only occurred accidentally, and immediately after
the needle returned to its habitual point of about
100 lbs., and resumed its oscillations between 50 9>s.
and 170 lbs. After having waited in vain to see
the motion regulate itself in a. more steady manner,
it appeared to us that the experiment was not sus-
ceptible of greater precision.
FRICTION OF THE WAGGONS. 139
The variation of the needle between 50 lbs. and
170 lbs. gave the medium of 110 lbs., and the three
waggons weighed together 14*27 tons; thus the
experiment gave ittot" ^^ 7*70 lbs. of resistance per
ton. But, as this mean was much too uncertain, it
appeared necessary to recur to another mode of
experiment.
In consequence, a convenient spot being chosen
on the Liverpool and Manchester Railway, near the
foot of the Sutton inclined plane, at the distance of
1 1^ miles from Liverpool, the level of it was taken
with strict accuracy in tenths of an inch, and the
experiments were begun on the principle we are
about to explain.
Sect. IIL Of the friction of carriages^ determined
by the circumstances of their spontaneous descent
and stop upon two consecutive inclined planes.
Suppose a system of two wheels joined together
by an axle-tree fixed invariably to each (fig. 31),
and loaded with a given weight resting at N, on a
chair on which the axle-tree may turn freely. Let
this system be placed on an inclined plane, along
which it is liable to roll. Again, at the foot of the
first plane, let there be another inclined plane con-
tinuing the former, and on which the rolling body
may continue its motion. Finally, suppose that the
140 CHAPTER V.
former of the two planes be sufficiently inclined to
cause the body placed upon it to roll down spon-
taneously, and by its own weight; and that the
second, on the contrary, though descending in the
same direction, be so slightly inclined that the
body, were it simply placed upon it, would be kept
still by the friction.
In these circumstances it is plain that the body,
abandoned to itself, will first roll down the first
inclined plane, accelerating its velocity gradually,
and that on reaching the second plane, its motion,
on the contrary, will slacken by degrees, till having
exhausted its acquired velocity, it finally be brought
to rest.
K the body experiences a considerable friction, it
will assume little velocity in its descent on the first
plane, and will promptly come to a stand on the
second. If, on the contrary, the friction has but
little intensity, the body will acquire a great ve-
locity on the first plane, and will prolong its course
considerably on the second. Comparing, then, the
height which the body has descended, with the
distance it has traversed before stopping, it will be
possible to recognise what intensity of friction it has
been submitted to in its course.
To obtain an analytical relation giving the so-
lution of this problem, it will be proper first to
form the equation of the motion of the body on the
two planes, and therefrom to deduce the velocity
FRICTION OF THE WAGGONS. 141
it will acquire in descending the first plane, and the
distance it will traverse on the second, in virtue of
that velocity.
Hence, the inquiry will comprise three successive
questions: 1st. To determine the effective accele-
rating force to which the centre of gravity of the
system will be subject in its motion ; 2nd. To de-
duce from this the velocity acquired by the moving
body at the foot of the first plane ; and 3rd. To
conclude finally the distance it will have traversed
on the second plane at the moment when the
friction shall have reduced its velocity to nothing.
The determination of the effective accelerating
force required, will be effected by means of the
principle that the motive forces applied and ef-
fective must be in equilibrio, that is to say, must
have their resultants equal and opposed, as well as
their momenta equal and opposite when the effective
forces are taken in the contrary way to their di-
rection.
Now, the motive forces applied to the system,
are :
1st. The weight of the body of the waggon
resting on the chair of the axle-tree, and which we
will call P. This force, acting vertically, will de-
compose into two others : one, in the direction of
the plane, will have an inunediate effect, and will
draw the body along the plane ; the other, per-
pendicular to the direction of the plane, will pro-
duce a pressure of the chair upon the axle and of
142 CHAPTER V.
the rim of the wheel upon the rail, and will conse-
quently cause on each of these points a friction, of
which we shall presently express the effect. If we
call & the angle of the plane with the horizon, the
first of these two forces will be P sin. 6\ and the
second P cos. ff ^ and the two together may replace
the primitive force P.
2nd. The weight of the system of the two rolling
wheels, with their axle. We will call this force
p, and will also replace it by two others p sin. d*
and 'p COS. 6i the one parallel, the other normal to
the plane.
3rd. The adhesion of the wheel on the rail at T.
This force acts along the plane contrariwise to the
motion oi translation. It is this force which pro-
duces the rotation of the wheel, by preventing its
circumference from sliding without turning during
the motion along the plane. We will express this
force by the weight T, which shall be equivalent
to it.
4th. The resistance of the air against the surface
of the system set in motion. Experience has de-
monstrated that this force is proportional to the
square of the velocity, and we will, in consequence,
express it by Qi;*, Q being the weight which re-
presents its intensity against the known surface of
the moving mass, in the case of 1;= 1 .
5th. The normal force P cos. dl which has been
mentioned above, produces a pressure of the chair
against the axle, and thus its effect will be to cause
FRICTION OF THE WAGGONS. 143
a friction at the point of contact. But as expe-
rience has proved that the friction of bodies sliding
on each other is a force proportional to the pres*
sure, and independent of the velocity or the extent
of the surfaces in contact, we will express the
friction in the present instance by f P cos. dl f
being a constant quantity; and that force will act
tangentially to the circumference of the axle, and in
the direction contrary to the motion of rotation.
6th. Lastly, the same force P cos. 6l and more-
over the force 'p cos. 6' produced by the weight of
the wheel, will exert a pressure at the point of
contact T of the wheel on the rail. There will
result from this pressure a friction at T ; but as at
this point the two surfaces in contact do not slide,
but merely roll one upon the other, the friction
produced will be of the second species. And, as it
is known from Coulomb's experiments, that the
intensity of this friction is inversely as the diameter
of the wheel, we will express it by
/'(P+ii)cos. «'X-^;
f being a constant quantity, which is easily de-
duced from the direct experiments made on this
subject, with wheels of 3 feet diameter, or of 1*5
feet radius. This force, in fine, will act tangentially
to the circumference of the wheel, and contrarily to
the motion.
Such are the divers motive forces applied to the
svstem.
144 CHAPTER V.
On the other hand, if we express by g the
gravity ; by ^ the effective accelerating force which
produces the motion of translation of the centre c
of the wheel ; by -^ the effective accelerating force
which produces the rotation of a point of the wheel
situated at the distance 1 from the axle, and, in
fine, by -&^ the momentum inertise of the wheel,
it is plain that the mass of the body being >
the effective motive force which produces the motion
of translation will he
and the momentum of the effective motive force of
the motion of rotation, will be
9 ^
Consequently, since the motive forces effective and
applied ought to be in equilibrio, as well in virtue
of their direct intensities, as in virtue of their mo-
menta about the axis of rotation, we shall have,
expressing by R and r the radii of the wheel and
axle, the two following equations :
P sin. e'^p sin. fl'-T-Q v^-^^4^,
TR—fFr COS. e'-f (P+i>) cos. 0'= ^ k^ ^.
Furthermore, as the velocity of the circumference
FRICTION OF THE WAGGONS. 145
of the wheel is equal to the velocity of translation of
the centre, it follows that the velocity of rotation
of a point situated at the distance 1 from the axis
of the wheel will be to the velocity of translation in
the ratio of 1 to R ; and, consequently, the same
relation will exist between the accelerating forces, or
^=R
Substituting then this value in the second of the
two equations above, and deducing the value of T,
we obtain, firstly,
T=/ P COS. e' . J +r (P+P) COS. «' • 4 +f • gl *•
Supposing the planes but little inclined, we have
very approximatively cos. 5" = 1. Besides, if we
make
/' p ^ +r (p+p) ^ =f(p+p).
the expression of the quantity T will become
Consequently, substituting this in the first equation,
we derive in fine for the value of ^,
*^7r^p — fc^(^^^-''--^-pf7^^'
^V+J' R^
As the weights P and p are known, as well as the
force Q, which expresses the resistance of the air,
L
146 CHAPTER V.
at the unit of velocity ; as, besides, the momentum
inertiae - k^ ib determined d priori, and as all these
quantities are constant, we may, in order to sim-
plify, make
Q , 9 9
— J— = a ana "^ j^ = -z — : — =: g .
+ P ^ 1 4_ P _*: l+« ^
Then the accelerating force to which the motion of
translation of the system is subjected, will be de-
finitively
4^ = g' (sin. 0'-f-qv^;
and the motion of translation of the moving body
may be considered as produced in spabe, by virtue
of that force alone.
The foregoing gives then the solution of the first
portion of the problem, namely, the determination
of the accelerating force. It now remains to deduce
from the knowledge of the accelerating force, the
velocity communicated to the mass by its descent
on the first plane, and the distance to which it will
be driven on the second plane by virtue of that
velocity. In order to effect this, we will first con-
sider the motion on the first plane.
Let X be the distance traversed on the plane,
when the body has acquired the velocity v; the
quantity (f> being the accelerating force of the mo-
tion, and that accelerating force being equally ex-
V dv*
pressed in general by the expression ""j"* we have
FRICTION OF THE WAGGONS. 147
V dv
or making for a moment, sin. 6' —f'=^ h\
V dv
This will be then the equation of the motion. In-
tegrating it, and observing that the velocity is null
at the point of starting, or that a?=o gives v'=^o^ it
will be replaced by the following,
2«-^ = log. wh' ■•
or, expressing by c = 2* 7 1828 18, the base of the
Neperian logarithms, it will be
y
which gives
fills'* — 1
qv'= b -jjp:
c«^«^' =
e"" *
This relation then makes known the velocity ac-
quired by the body after it has traversed the dis-
tance X on the first plane.
It will be recognised therein that the greater x is,
the greater also becomes v ; and for x=oo we have
qv^=b' or ff>=o; that is to say, the motion, as it
continues, approaches more and more to uniformity.
But it will be remarked that, since the value of qv^
may be written under the form
qv^=V (1 "^iS^)'
148 CHAPTER V.
the motion will be sensibly uniform as soon as x
becomes large enough to make the fraction of the
second member inconsiderable with reference to 1 ;
and as or is here an exponent, it is plain that this
condition will quickly be fulfilled. From this point,
then, we shall have
and the motion will no longer differ from uniformity
but by an inconsiderable quantity. This in fact, as
experience proves, does really take place within a
very short time.
The preceding inquiry gives then the velocity at
any point whatever of the first plane ; and if we
call /' the length of the plane, and V the velocity of
the body the moment it arrives at the bottom of the
plane, we see from the equation just obtained, that
this velocity will be
which solves the second part of the problem.
Now that we have the velocity of the moving body
at the foot of the first plane, and consequently at the
beginning of the second, since they are supposed to
be united by a continued curve, the question is to
determine at what point of the second plane the
body will stop, which will lead us to the definitive
solution of the problem.
To this effect must be considered the motion of
the body on the second plane. Calling 0'' the angle
FRICTION OF THE WAGGONS. 149
it forms with the horizon, as all the circumstances
of the motion remain the same as before, except
only that the inclination of the plane is less, we
shall have by analogy
—^ = 9 (sin. 0 ^f-qv^).
And as we have supposed that on the second plane
gravity is less than friction, that is to say, we have
sin. 0''<f, we will here make
sin. r-./=-.r.
Then the accelerating, or rather retarding force,
since it is negative, of this second motion, will be
expressed by
V dv ,
Integrating this equation then, and observing that at
the beginning of the plane the velocity is V, or, in
other words, that 07 = 0 gives i; = V, it will be re-
placed by the following, which is suitable to every
point of the motion.
(Consequently, if V stand for the distance traversed
by the body on the second plane, at the moment
when its velocity becomes null, this equation will
still subsist if we make in it at once
, 1; = 0.
Thus it will become
150 CHAPTER V.
2 qgr = log.
V'+qV
or
^ — 1 + -yT >
and putting for gV^ its value concluded from the
motion on the first plane, this equation will become
6' e**^'" — 1
!L I 1 ^jjf'i'
If' — e^9ti' _ 1 «
Finally, if instead of g\ b' and b'\ their values be
restored, and if, moreover, h' stand for the vertical
height which the body has descended on the first
plane, and h'' the vertical height which it has de-
scended on the second, which gives
Y and sm. 5 = -w?
sin. 5'= -v" and sin. 5''= -v/ >
the relation just obtained above will become
K-fV _ r_ e"^' -1 ?^
•^ e*^' — 1
This is the definitive relation between the co-ordi-
nates of the points of departure and arrival of the
moving body, the various data of the problem and
the friction sought.
When in this equation we suppose 9=0, the
second member reduces itself at first to -, but
FRICTION OF THB WAGGONS. 151
it changes to
and dividing by y — 1 , it becomes
r_ y^--»+y--^» + y---» +1
r r
which for 5=0 or y= 1 , reduces itself to 7?/ Xp = 1 .
Wherefore in this case, that is to say if the motion
took place in a vacuum, the above relation would
become
/r-r^^^ whence /—^rpyr-
Consequently, we should then have the friction re-
quired, by dividing the sum of the vertical heights
which the body has descended, by the sum of the
spaces it has traversed; and it will be remarked
that in this case, since there would be no resistance
of the air, the motion of the body on the first plane
could never attain uniformity.
We have seen what the general relation becomes,
on supposing f =0 ; if moreover we make/=o, that
relation reduces itself to
A' + r = o or r=-h'.
Consequently were there neither friction nor re-
sistance of the air, the moving body would rise
on the second plane, supposing it inclined contrari-
152 CHAPTER V.
wise to the first, to a height equal to that from
which it has descended ; and we quote these results
because, being easily deduced from the direct ex-
amination of each supposition, they serve here to
verify the calculation.
To return to the general formula, making in it
*— 7" "TUP ^
^ cJ^i - 1
we perceive that it may be written under the form
ft-K'- ^ '
whence is derived for the value of the friction /,
•^-r+rY *
Thus, when, after having submitted a body of a de-
termined weight, to the above experiment, on two
planes of known inclination, the quantities K X h"
and r shall have been found, it will suffice to cal-
culate the corresponding value of Y, and introducing
it with the other data in the expression of/, we may
deduce the value of this latter quantity, which will
be the friction sought.
This method has the advantage of not depending
on the execution more or less imperfect of an in-
strument, and of being applicable to considerable
trains of waggons, as we shall presently apply it.
FRICTION OF THK WAGGONS. 153
Sect. IV. Experiments on the friction of waggons.
According to this principle, experiments were
undertaken on one of the inclined planes of the
Liverpool and Manchester Railway in the following
manner.
From a point taken on the Sutton inclined plane,
at 50 chains or 3300 feet from the base of that
plane, were measured 34 distances of 10 chains or
330 feet each. At each of these points was set
up a staff numbered, and its level accurately taken.
The following are the admeasurements of the level-
ling, expressed in feet and decimals of feet.
The staves have since been replaced by perma-
nent posts, which are distinguished, by red marks,
from those which serve to indicate the miles of the
road.
154
CHAPTER V.
Total difltance
Nnnibcn of
from the Itt
Total fall below the Ist post, in feet
the posts.
post, in feet.
and decimals of feet.
feet.
feet. Point of Btarting.
0
0
0
1
330
3-47
2
660
707
3
990
10-62
4
1320
14-36
5
1650
1817
6
1980
21-77
7
2310
25-53
8
2640
28-98
9
2970
32-07 r Foot of the inclined
10
3300
34*61 < plane, or rather mid-
11
3630
35-06 [die of the curve.
12
3960
35-19
13
4290
35-23
14
4620
35-37
15
4950
35-71
16
5280
36-17
17
5610
36-44
18
5940
36-66
19
6270
36^80
20
6600
36*92
21
6930
37-06
22
7260
37-14
23
7590
37*22
24
7920
37-37
25
8250
37-34
26
8580
37-63
27
8910
3792
28
9240
38-14
29
9570
38*35
30
9900
38*54
31
10230
38*67
32
10560
38*77
33
10890
38*92
34
11220
39-08
On the ground where these experiments were
made, a little beyond the foot of the inclined plane,
FRICTION OF THE WAGGONS. 155
the waggons had to cross three junction roads, each
of which required the passing over three switches.
This made in all nine switches, either on one side
of the rails or on the other. On passing over each
of these obstacles, the waggons received a jolt from
the unevenness of the road, and must have been
retarded in their progress. The ground, therefore,
is not favourable to the experiments, and tends to
include in the friction the inevitable imperfections
of the road.
The waggons employed in the experiments are
of the following construction. They consist of a
single platform supported on four springs; the
wheels are 3 feet in diameter, and are fixed to the
axle-tree, which turns with them ; the body of the
carriage rests upon the axle-trees, but outside of
the wheels ; that is to say, that the axles are pro-
longed through the nave in order to support the
carriage. At the bearing they are turned down to
1} inches in diameter. By this disposition the
body of the axle-tree preserves its usual strength to
resist the shocks received by the wheels in the
motion, and the bearing- may at the same time be
reduced to the slender diameter of If inches, be-
cause that part has nothing but the body of the
waggon to sustain. The chair is armed with a
piece of copper at its rubbing point on the axle,
and the grease, placed in a small cast-iron box
above the axle, runs on it slowly, but without in-
terruption, during the whole of the motion. This
156 CHAPTER V.
grease-box, filled every morning, is sufficient for the
need of the whole day. In the experiments no
alteration whatever was made in these dispositions,
every thing being left the same as it is in the daily
work, both with regard to the waggons and to the
rails. Among the waggons there are some, the
axle-bearings of which, instead of being from one
end to the other of a uniform diameter of If
inches, are thickened near the frame of the carriage
by f inch, and are, on the contrary, diminished as
much at the other end. The axle-bearing thus
consists of three cylindrical parts equal in length,
and the diameters of which are 2^, If, and If
inches.
The object of this disposition is to leave the
mean diameter of the axle-bearing the same as
before, but to transfer, however, the greatest force
to the point which seems to suffer the most. These
axles, few in number, are but an essay of which
experience has not yet confirmed the advantage.
As all the experiments we are about to report
have been made in a manner perfectly similar, we
shall give the details merely of one of them, and
shall afterwards collect in a Table the results which
all have produced, with the elements of the calcu-
lation for each of them.
On the 1st of August, 1834, 24 loaded waggons
taken indiscriminately, were conveyed to the ground
of the experiments by the engine Atlas. The weight
of the 24 waggons, taken accurately with their load,
FRICTION OF THE WAGGONS. 157
amounted to 104*50 tons, and that of the tender-
carriage of the engine, which remained attached to
the waggons, was 5*50 tons, forming altogether an
assemblage of 25 carriages, weighing 110 tons.
The middle carriage of the train being placed on
the plane precisely opposite the starting point or
post No. 0, and the engine being removed pre-
viously, the brakes were taken off at once at a
signal given, and the 25 waggons committed to
gravity on the plane. They continued their motion
to 108 feet beyond the post No. 32, having thus
traversed on the first plane a distance of 3300 feet
with a vertical fall of 34*61 feet, and on the second
a distance of 7368 feet with a fall of 4*21 feet. In
this experiment then we have :
r=3300, V=34-61, r=7368, r=4-21.
We have just seen, besides, that the weight of the
train was
P+l>= 110 t, or in lbs. P+p= 110 X 2240 lbs.
It is also known that the quantity e, which ap-
pears in the equations, and which expresses the
base of the hyperbolic logarithms, has for its value
^ = 2-71828;
and that the gravity g, expressed in English feet
per second, is
g = 3S feet.
Finally, the resistance of the air per square foot of
158 CHAPTER V.
surface, at the velocity of 1 foot per second, is
expressed, as we have seen, for 6=1*05, by
Q=00125;
and the resisting surface of the train, measured as
has been explained in the preceding chapter, viz.,
at 70 square feet for the transverse section of the
train and 10 square feet per waggon, amounted in
all to 320 square feet.
Nothing remains then, in order to have all the
elements of the calculation, but to determine the
value of the quantity n, viz.
k
.9
n =
This determination is easy ; for p is the weight of
aU the wheels with their axle-trees, or as many times
'85 ton as there are carriages, and P+ j) is known.
Moreover, considering the wheel as a full cylinder,
in which the weight of the axle should compensate
for the void existing between the spokes, we should
have approximatively, from the theoretical deter-
mination of momenta inertise,
but some experiments made on axles separated from
the carriage, with a view to determine precisely their
centre of oscillation, having given for that fraction
the number '54, we will adopt that value. We shall
have then
FRICTION OF THE WAGGONS. 159
R2 — ^^ >
and consequently the expression of the quantity n
will here become
^^ 25 X -85
n = -54 X — jjQ — = 104.
The'se various values being substituted in the ex-
pression of Y, give
Y= 1-7040;
and consequently the friction is
/= 002635 or 590 lbs. per ton.
The calculations relative to the other experiments
are performed in a maimer entirely similar. Only,
in three of them, to wit, the experiments VIII. IX.
and X., which, besides the waggons, included also
an engine, the value of / was first found, as before,
and the friction of the whole train was concluded
from it. But it was not till after having subtracted
the friction proper to the engine itself, in conse-
quence of a special experiment made immediately
before and on the same spot, that the remainder
was divided by the weight of the train, exclusive
of the engine ; and thus was obtained the friction
per ton proper to the waggons. The special ex-
periment here noticed, and from which we derive
the friction proper to the engine, at the moment of
the observation, wiD be reported further on.
In the experiments V. and IX. .the train could
160 CHAPTER V.
not be made to start precisely from the post No. 0,
and the vertical fall and distance traversed varied in
consequence ; but account has been carefully taken
of this in the calculation, as may be remarked in the
Table.
During all these experiments the weather was fine
and calm, and, as has already been said, nothing
had been changed in the ordinary state of the
waggons or the rails.
FRICTION OP THE WAGGONS.
J
jJlJ
lllli
I
I
j
5 ? T" ?> f 9 "P *
J'oSSSSSS
||2?|f"|
•11
illll-fjnlltl
lllliiiHiiiii
Hi
5S2S2
I!
timtii t i
162 CHAPTER V.
From these experiments, the mean friction of the
waggons, taken independently of the resistance of
the air, amounts to -g^ of the gross weight of the
waggons, or to 5*76 fi^s. per ton; but to simplify
the calculations, we will take it at 6 lbs. per ton,
which makes s^-g of the weight of the waggons.
These are the results which ought to be used,
when, for the resistance of the air, the determina-
tion deduced from the most recent and most exact
experiments on the subject is used, and when ac-
count is taken, as it ought to be, of the length of
the prism formed by the train in motion, as well as
of the effects of the air against the rotation of the
wheels and the accessory parts of the waggons.
But if the calculation were limited to the use of
the determination of Borda, which does not enter
into the consideration of the diminution of re-
sistance of lengthened bodies, and if account were
taken only, as is the custom, of the resistance of the
air against - the front surface, or transverse section,
of the train ; that is to say, if the calculation of the
foregoing experiments were performed anew, with
Borda's datum, and giving to S the value indicated
by the waggon of greatest section, then it would be
found that the friction of the waggons should be
taken at 7 lbs. per ton.
It appears then, from this result, that for the
mean velocity of the trains during the experiments,
it would be indifferent to compute the friction of
the waggons at 5*76 lbs. per ton, taking account of
FRICTION OF THE WAGGONS. 163
the real resistance of the air and of its effects against
the accessory parts noticed above, or to take the
friction of the waggons at 7 9>s. per ton, accounting
merely, according to Borda, for the resistance of the
air against the waggon of greatest section. On the
other hand, as, during the work of the engines, their
velocity is so much the greater as the train they
draw is less considerable, whence the resistance of
the air increases as the friction of the train di-
minishes, it will equally be found that either of
the two preceding calculations leads to very nearly
the same result, for the total resistance opposed by
the moving train, and that it is only in cases of
extreme velocity that the two modes of calculation
present a notable difference.
Without any important error then, the second
of the two modes of calculation may be used. It
IB that which we had indicated in a former work
(Theory of the Steam Engine) , when unacquainted
with any otiher researches on the resistance of the
air than those of Borda ; but now that M. Thibault's
experim^its have enabled us to employ a method
much more exact, we have duly given it the pre-
ference, remarking at the same time that the defini-
tive results of the calculations will not thereby be
notably changed.
This satisfaction, however, attends the coincidence
which we have just noted, viz., that an error in the
valuation of one of the two elements of the total
164 CHAPTER V.
resistance of the trams, would cause no important
error in the calculation of the effects of the engines.
Sect. V. Of the causes of variation in the friction of
carriages.
In the preceding experiments we employed as
much as possible trains composed of a great number
of carriages, because there often exist great dif-
ferences between the individual frictions of two
waggons of similar construction, and that it is only
by uniting them in numerous trains, that the com-
pensation which establishes itself between their dif-
ferent frictions can lead to a uniform mean result.
We must add, moreover, that the determination
of the friction, which we have just obtained, refers
to the waggons whose construction has been indi-
cated above, and to the state of the Manchester and
Liverpool Railway. As, however, on other lines,
different circumstances may occur, it becomes ne-
cessary to notice here the variations which may
result from them in the friction of the carriages.
The causes of the variation of friction are of four
kinds: 1. the construction, the maintaining, and
greasing of the carriage ; 2. the state of the rails ;
3. the diameter of the axle-bearing and that of the
wheel; and, 4. the proportion between the total
weight of the carriage and that of the body of the
carriage taken separately.
FRICTION OF THB WAGGONS. 165
That the influence of these four causes may be
quite clear, we will refer to what has been said in
sect. III. of this chapter. It was there seen that
the friction of a carriage consists of two parts:
one owing to the friction of the axle, which de-
pends only on the weight of the body of the
carriage ; and the other owing to the rolling of the
wheel on the rail, which depends on the total weight
of the carriage. It has been seen that the first of
these frictions produced against the motion a force
which we have represented by
and the second a force represented by
/" (P+p) 1-.
f denoting the coefficient of the friction of axles,
/" that of the rolling friction, r the radius of the
axle-bearing, and R that of the wheel. But in order
to simplify, we have replaced the two expressions by
a single one, making
/T^+r(P+/>)^=/(P + p);
that is to say, instead of entering into the consider-
ation of these two separate frictions, we have been
content to consider the single force resulting from
their union, and which we have supposed propor-
tional to the total weight (P+p) of the carriage.
166 CHAPTER V.
But it is now requisite to direct a moment's
attention to this expression.
Ist. Since the quantity/' expresses the friction of
the axle on its chair, for a given weight of the body
of the carriage, it is plain that the more carefully
roimded, polished, and greased the axle is, and the
more easily the metals in contact slide upon one
another, the less the coefficient/' will be. On this
first term, then, is felt the influence of the mode of
construction and greasing of the carriage.
2d. From the same motive, the influence of the
state of the rails, and of the perfect roundness of the
wheels is felt on the factor f'\ which expresses the
coefficient of the rolling friction.
3d. The smaller the diameter 2r of the axle-bear-
ing, the. more the first term, or resistance due to the
friction of the axle, will be diminished ; and simi-
larly, the more the diameter 2R of the wheel shall be
augmented, the more thereby will be diminished the
two partial frictions which take place, either on the
axle or on the raU.
4th. Finally, between two carriages wherein all
the preceding conditions were strictly identical,
some difierence might yet arise in the value of the
definitive friction / In efiect, the preceding re-
lation giving
_ , ^ ^ r „ \
f=fY^' R +/" R'
it is visible that the invariability of the quantities/',
f'\ r and R will not prevent a variation in the value
FRICTION OF THK WAGGONS. 167
of /, according to the magnitude of the fraction
p
-= , that is to say, according to the ratio be-
F + p
tween the weight of the body of the carriage and
the total weight of the waggon.
From these divers observations, it becomes clear
that on the same railway, the definitive friction /, of
which we have found above the mean value 6 fibs,
per ton, may vary according to the state of the
waggons, the state of the rails, and the proportion
of the load to the weight of the carriage ; and that
between carriages differently constructed, the fric-
tion may vary yet again, according to the diameter
of the axle-bearings and of the wheels.
The preceding considerations show that the valu-
ation of the friction, which we obtained above, ought
to be imderstood only of carriages similar to those
which were submitted to experiment, and subject to
like conditions, viz. with iron axles, turning on
brass chairs and provided with self-acting grease-
boxes ; with three-feet wheels and axle-bearings 1 f
inches ; with the use of a well-kept railway, and
finally with the usual proportion of about ^ between
the weight of the body of the loaded carriage and
the total weight of the waggon. Were these condi-
tions materially altered, a new determination of the
friction would become necessary.
CHAPTER VI.
OF GRAVITY ON INCLINED PLANES.
We have seen, in the preceding chapter, how the
resistance caused on a railway by the friction of the
waggons may be valued. But it sometimes happens
that this friction is the smallest part of the total
resistance which the engine has to overcome, in
order to effect the motion of the train. This case
occurs when the way is not level, and the train
is obliged to ascend an acclivity. The resistance
then caused is, as every one knows, much greater
than on a level line, and in consequence it becomes
necessary to take account of it in the calculations.
When a body is placed on an inclined plane, the
weight which urges it, and which always acts in a
vertical line, is decomposed into two forces : one
perpendicular to the plane, and which measures the
pressure produced against the plane, by virtue of
the weight of the moving body, and the other ^
parallel to the plane, and which tends to make the
body slide or roll along the declivity. The latter
force, which we will call the gravity along the plane,
would inevitably drag the body towards the foot
of the declivity, were it not counteracted by a con-
GRAVITY ON INCLINED PLANES. 169
trary force. When therefore a train of waggons has
to ascend an inclined plane, the moving power must
apply to it: firstly, a force able to overcome the
friction of the waggons themselves; and again, an-
other force able to overcome the gravity in the
direction of the plane. If, on the contrary, the
mover draw the train of waggons down the plane,
then, in order to produce the motion, it will evi-
dently have to apply only a force equal to the dif-
ference between the friction proper to the waggons
and the gravity, since the latter force then acts in
the same direction as the mover.
When a body of a given weight is set on a plane
of a given incUnation, we know that, in order to
obtain the gravity of the body along the plane, its
weight is to be multiplied by the fraction which
expresses practically the inclination of the plane.
Thus, for instance, on a plane inclined ^, that is
to say, on a plane which rises 1 foot on a length of
89 feet measured along the acclivity, the gravity of
1 ton, or 2240 lbs., is
??^ = 25-2 lbs.
89
Moreover, when a train of waggons ascends an
acclivity, the engine has not only to surmount the
gravity of the waggons of the train, but Ukewise its
own gravity and that of the tender which follows it ;
and these forces do not present themselves when the
motion takes place on a horizontal line. It is then
170 CUAFTBR VI.
on the total weight of the train, that is, including
engine and tender, that the resistance caused by
gravity on acclivities is to be calculated.
If it be supposed, for instance, that a train of 40
tons, tender included, be drawn up a plane inclined
^, by an engine weighing 10 tons, it is clear that
the definitive resistance opposed to the motion by
the train wiU be
40 X 6 fts. = 240fi^s., friction of the carriages
at 6 lbs. per ton . . . 240fi^s.
50 X ^9^ = 1 258 lbs. , gravity of the 50 tons
of the train (reduced to
lbs.) on a plane in-
cUned^,tobeadded 1258
Total resistance arising from friction and
gravity 1498 fts.
If, on the contrary, the same train had to descend
a plane inclined fwb' ^^^ resistance it would then
offer would be
40 X 6 fi^s. =240 9>s., friction of the waggons 240 lbs.
50xf^^=112fts.,gravity of the train, to
be deducted 112
Definitive resistance arising from friction
and gravity 128 fts.
In general, let M be the weight of the train, in
tons gross and including the tender ; let m be the
GRAVITY ON INCLINED PLANES. 171
weight of the engine, expressed also in tons ; k the
friction of the waggons per ton, expressed in 9>s., as
has been explained in the preceding chapter; finally,
let g be the gravity, in 9>8., of 1 ton on the plane in
question. It is clear in the first place, firom what
has been said above, that the quantity g will be
equal to 2240, multiplied by the practical inclina-
tion of the plane ; so that if - express that inclina-
tion, or the ratio of the height of the plane to its
length, we shall have, to determine ^, the equation
2240
This premised, the friction of the waggons will
have for its value
fcM.
Again, since g expresses the gravity of 1 ton, it is
plain that
g (M + m)
will represent, in lbs., the gravity of the total mass,
train and engine, placed on the inclined plane.
Thus, according as the motion takes place in
ascending or in descending, the total resistance,
in 9>s., offered by the train on the inclined plane,
will be
*M ± jf (M + m) = (fc ± jf) M ± jrm,
an expression in which the sign + belongs to the
ascending motion, and the sign — to the descending
motion, of the train.
172
CHAPTER VI.
It will always be easy then to obtain the number
of lbs., which represents the resistance opposed by
a train in motion on a plane of a given inclination.
This is the only result which we want at this mo-
ment ; but as the intervening of inclined planes on
railways brings with it some particular considera-
tions, we will return to this subject further on, in
order to solve the various problems that may occur.
We have said above that when a body is placed
on an inclined plane, its weight is decomposed
into two forces, one acting along the declivity, as
has been explained, and the other acting normally
to the plane, and measuring the pressure which the
weight of the body produces on the plane. In this
case then, the weight of the train, with reference to
the sustaining plane, is now expressed only by the
normal component just mentioned, and not by the
total weight of the waggons. Consequently, to be
thoroughly accurate, instead of then reckoning the
friction of the waggons from their total weight, it
ought to be reckoned only from the normal com-
ponent on the plane. This force is to the weight of
the waggons, as the horizontal length of the inclined
plane is to its length measured along the declivity.
But as there never occur, on railways, planes so
much inclined as to render the difference between
those two lines not wholly inconsiderable, it is per-
fectly useless to make a distinction on that head.
For instance, on a plane whose practical inclina-
tion shall be y^, which is a steep ascent for a rail-
GRAVITY ON INCLINED PLANES. 173
way, we find by geometry that the horizontal length
of the incUned plane will be to its length measured
along the declivity, in the ratio of the numbers
99995
100000"
The difference then between the absolute and the
relative weights of the waggons, is always an inap-
preciable quantity in practice. For this reason, in
all cases, we shall reckon the friction of the waggons
placed on inclined planes, at the same rate as if they
were placed on a level line.
CHAPTER VII.
OF THE PRESSURE PRODUCED ON THE PISTON BY
THE ACTION OF THE BLAST-PIPE.
Sect. I. Of the effects of the Blast^pipe.
Wb have just examined and measured successively
several of the resistances which are opposed to the
engine in its motion, viz., that of the waggons along
the rails, and that of the air against the trains.
But among other resistances which the piston has
yet to overcome, is one arising from the disposition
of the engine itself, and of which it will be proper
to treat before proceeding further.
The steam, after having exerted its action in the
cylinder, might escape into the atmosphere by a
large opening. It would then be possible for it
entirely to dissipate itself in the air, during the
time the piston takes to change its direction. Con-
sequently the steam would in nowise impede the re-
trograde motion of the piston, whatever might be the
velocity of the piston. But the disposition adopted
is contrary to this. The steam, on leaving the cy-
linder, has no other issue towards the atmosphere
than an aperture exceedingly narrow ; nor can it,
by that aperture, escape totally within the time of
PRESSURE IN THE BLAST-PIPE. 175
one Btroke, except by assuming a very considerable
velocity in its motion. For this, the steam in the
cylinder must necessarily be at a pressure sensibly
greater than that of the atmosphere into which it
flows ; and as the pressure of the steam while flow-
ing acts in all directions, and consequently against
the piston, it results that the latter, instead of having
simply to counteract the atmospheric pressure, finds
an additional one to overcome, which is to be added
to the divers resistances already measured.
This new cause of resistance might, as has been
said, b^ in a great measure suppressed, by enlarging
sufficiently the outlet of the steam. But to do this
would be to lose one of the most active causes of
the definitive efiect of the engine ; for the object of
the disposition of which we treat is to excite the fire
sufficiently, and to produce, in a boiler oi small
dimensions, the very great quantity of steam requi*
site for the .rapid motion of the engine. To this
end, the waste steam is conducted to the chimney,
and thrown into it by intermittent jets, through a
blast-pipe or contracted tube, placed in the centre
of the chimney and directed upwards. The jet of
steam, as it rushes with force from this aperture,
rapidly expefe the gases which occupied the chim-
ney. It, consequently, leaves behind it a vacuum ]
and this is immediately filled by a mass of air rush-
ing through the fire-grate into the space where the
vacuum has been made. At every a^iration thus
produced, the fuel contained in the fire-box grows
176 CHAPTER VII.
white with incandescence. The effect then is similar
to that of a bellows continually urging the fire ; and
the artificial current created in the fire-box by this
means is of such efficacy for the vaporization, that
were the blast-pipe suppressed, the engine would be-
come almost useless, which proves that the current
of air attributable to the ordinary draught of the
chimney is in comparison but very trifling.
We shall return in the sequel, when speaking of
the vaporization of the engines, to the effects of the
blast-pipe relative to the production of steam. At
present we have only to consider its effects relative
to the pressure it causes against the piston.
For this purpose we must first examine how this
pressure, necessary to the outflow of the steam, is
produced in the cylinder. At that moment when
the eduction-pipe opens, and the steam begins to
escape into the atmosphere, its pressure is yet the
same as it was immediately before, when it served
as the motive force to produce the motion. The
latter pressure then is that which takes place at the
first moment, and which, by reason of its excess
above the atmospheric pressure, produces the efflux
of the steam. But as that pressure is very con-
siderable, and as the gases acquire, as is well known,
very great velocities, even under very weak motive
or effective pressures, it follows that at this moment
the steam necessarily rushes from the cylinder with
an enormous velocity ; and as, moreover, its density
is then very considerable, it results that the greater
PRESSURE IN THE BLAST-PIPE. 177
part of the steam escapes immediately, or at least in
a very short space of time. However, as the efflux
takes place, the pressure of the remaining steam
diminishes, as well as its density. Consequently
the issuing velocity of the steam and the quantity
of it which flows out in a given time diminish at
the same time. A point then occurs at which the
spontaneous efflux of the steam by the blast-pipe
no longer exceeds the velocity which, by reason of
the size of the orifice, corresponds to the velocity
of the piston in the cylinder. Beyond this point
the issuing velocity of the steam cannot diminish,
for the piston, continuing its stroke, forces it out
of the cylinder as rapidly as itself performs its
motion. It is then the velocity of the piston which
fixes the lower limit of the velocity of efflux of the
steam ; and consequently the smallest efiective pres-
sure that can take place in the cylinder is that which
is capable of producing, in the efflux of the steam
by the blast-pipe, a velocity corresponding to that
of the piston.
Thus, at the moment of the opening of the educ-
tion-pipe, there is a tendency to produce in the
blast-pipe an effective pressure equal to that which
the steam had during its motive action in the
cylinder ; but the duration of this extreme pressure
is in a manner instantaneous. It immediately
diminishes rapidly, and soon attains its inferior
limit, which afterwards subsists till the end of the
stroke; and then is produced in the blast-pipe a
N
178 CHAPTER VII.
uniform effective pressure, corresponding to a ve-
locity of efflux of the steam measured by the velo-
city of the piston.
Again, as the two cylinders communicate with a
single blast-pipe, it happens that each cylinder
transmits to the blast-pipe alternately steam, first
at a very high pressure, and then at a low one ; and
these effects succeed each other in such sort, that
when one cylinder supplies steam at a low pressure,
the other on the contrary gives it at the higher pres-
sure. As these alternations are exceedingly rapid,
there must result in the blast-pipe a certain mean
pressure, which forms in a manner a factitious
atmosphere, in which the two pistons work. This
factitious atmosphere it is necessary to know; for
evidently as soon as it becomes known, it will
suffice to substitute it, in the calculation, for the
natural atmosphere, to take account, without any
other difficulty, of the resistance exerted against
the piston by the action of the blast-pipe.
Before proceeding further, we will therefore ex-
amine how this mean pressure existing in the blast-
pipe, must be modified according to the different
circumstances of the working of the engine.
1st. If the velocity of the piston increases, without
any other change being made in the engine, it is
visible, from what has been said above, that the
lower limit of the effective pressure in the blast-
pipe will increase ; and according to the principles
admitted in the flowing of fluids, it will increase
PRESSURE IN THE BLAST-PIPE. 179
nearly as the square of the velocity of the piston.
But on the other hand, it will be seen further on,
that with the same vaporization in the boiler,
the velocity of the piston cannot increase, without
the effective pressure in the cylinder diminishing
nearly in the inverse ratio of that velocity. Hence,
in the case before us, namely, that of an increase of
velocity of the engine without an increase of vapo-
rization, the inferior limit of the effective pressure in
the blast-pipe will augment in proportion to the
square of the velocity of the piston, and its superior
limit will diminish in the inverse ratio of the same
velocity. As we have seen besides, that the max-
imum pressure in the blast-pipe is of a duration
much less than the minimum pressure, it follows
definitively that the mean effective pressure in the
blast-pipe will receive an augmentation, simulta-
neous and in a certain proportion with the velocity
of the piston.
2d. If, the velocity of the piston remaining the
same, the vaporization of the boiler increase, it is
plain that the velocity of the piston can then re-
main constant, only because the steam arrives in
the cylinder with a total pressure augmented nearly
in the ratio of the vaporization, or with an effective
pressure augmented in a manner corresponding to
it. It is now therefore the superior limit of the
effective pressure in the blast-pipe, which .will have
an increase correspondent to the vaporization pro-
duced, whereas the lower limit of the same pressure
180 CHAPTER VII.
being always indicated by the velocity of the piston,
will on the contrary undergo no change. Thus,
in this second case, the mean effective pressure
in the blast-pipe must necessarily increase in a
certain ratio with the vaporization of the boiler.
3d. Finally, if the velocity of the piston remain
the same, as well as the vaporization of the boiler,
but if the orifice of the blast-pipe be diminished
without altering the area of the cylinder, it is clear
that the same velocity of the piston will then corre-
spond to an issuing velocity of steam by so much the
greater ; and that if, for instance, the area of the
blast-pipe be reduced to the half of what it was
before, the issuing velocity of the steam, corre-
sponding to the velocity of the piston, will be
doubled. But, from the principles of the efilux of
fluids, this double velocity will require a motive
or effective pressure nearly quadruple. Hence, in
this case, the inferior limit of the effective pressure
in the blast-pipe will vary nearly in the inverse ratio
of the square of the orifice of efflux of the steam ;
but the superior limit of the same pressure will not
vary, since it is always fixed by the pressure of the
steam during its action in the cylinder. Therefore,
definitively in this third case, the mean efiective
pressure in the blast-pipe will receive an aug-
mentation increasing in a certain inverse proportion
of the ori^ce of the blast-pipe.
These divers effects would no doubt be susceptible
of a solution more or less exact by calculation ; but
PRESSURE IN THE BLAST-PIPE. 181
considering their nicety and at the same time the
imperfectness of the theory of the efflux of fluids,
we deem it more useful for the applications, to
endeavour to determine them in a direct manner
and by observation. For this reason, we shall make
use of the preceding considerations, only to guide us
in the research of the laws which may be derived
fit)m experience in this respect.
We will nevertheless observe, that there is a
moment when the pressure in the blast-pipe pro-
duces no opposition against the motion of the
piston. This effect depends on the circumstance
that, from a disposition of the engine which we
shall explain in speaking of the lead of the slide,
the eduction-port of the steam is opened a little
before the piston has reached the bottom of the
cylinder. The result is, that during the short inter-
val yet left for the piston to traverse to finish its
stroke, the pressure in the blast-pipe is found acting
in the direction of the motion, instead of acting
against it. But as, nearly at the same moment and
from the same disposition, the steam of the boiler
comes in beforehand against the motion of the
piston, it follows that the resistance owing to the
blast-pipe is only replaced by a stronger resistance.
As however the velocity of the piston is then nearly
null, and as its action to produce the motion is
equally without efficacy, we will admit that the one
effect replaces the other, and shall enter on no
distinction in that respect.
182 CHAPTER VII.
Sect. II. Experiments on the resistance produced
against the piston by the action of the Blast-pipe.
To measure the resistance produced against the
piston by the action of the blast-pipe, and the modi-
fications it undergoes according to the circumstances
in which the engine works, we undertook a series
of experiments, which we are about to describe.
The blast-pipe of the engine Star being taken
out of the chimney, the extremity of it was cut at
the point where the cone was three inches in dia-
meter, and the removed part was replaced by a
bonnet conical at the bottom, and which was fitted
at this point with screws on the remaining portion
of the cone of the blast-pipe (fig. 36). At its upper
part, this bonnet changed into a quadrangular con-
duit aabb, each side of which was two inches and
a half in width, measured in the inside. Of the
four sides of this conduit, three were fixed, and
perfectly smooth on their inner surface ; the fourth
aa was moveable on a hinge c, and when pushed at
aV, towards the inside of the passage, in which it
moved with an easy friction, the steam-way became
narrowed by so much. Thus, when this factitious
blast-pipe was entirely open, it presented a square
orifice whose side was 2*5 inches, that is to say, an
area of 6*25 square inches ; and when the moveable
side was forced into the opening 1^ inches, the
efflux orifice was no more than 2*5 inches by 1
PRESSURE IN THE BLAST-PIPE. 183
inch, that is to say, was reduced to 2'5 square
inches of area. By this means, then, the orifice of
the blast-pipe could be altered at pleasure.
In order to execute this change easily, without
opening the chimney or stopping the engine, a rod
M'O, fixed on the moveable side of the blast-pipe,
communicated, by means of a lever MOQ, whose
fixed point was at Q, with a long rod Mm, whose
other extremity m reached to the engine-man's stand.
This rod Mm was composed of two parts : one,
ME, terminated by a nut E invariably fixed to the
rod; and the other, me, terminated, on the con-
trary, by screw-bolts which inserted themselves
into the nut, and thus united the two pieces into
one. The part me of this rod passed into a fork
PN, where it was maintained by two collars, to
prevent its sliding longitudinally. It then ter-
minated by a crank handle T. When a certain
number of turns were made with this handle, it
is plain that the screw e was made to penetrate
more or less into the nut E, and that, consequently,
the rod mM was shortened or lengthened. Thus,
as the point N was fixed, it is evident that the
moveable side of the blast-pipe was by so much
either drawn in or pushed out.
To measure precisely these shortenings or length-
enings of the rod, a fixed index i was attached to
the steam-dome of the boiler, and the upper surface
of the nut E was marked with divisions. When
therefore, by the motion of the handle, the nut
184 CHAPTER VII.
approached the fork N, its divisions passed suc-
cessively under the fixed index ; and consequently
the addition to the length of the rod might be
read immediately. The dimensions of the divers
pieces were such, that this increase of length in*
dicated precisely the contraction that had taken
place in the blast-pipe.
In order to obtain the pressure of the steam after
it had left the cyUnder, a brass tube of half an inch
in diameter, inserted into the pipe leading to the
blast-pipe, brought a portion of that steam into a
receiver, placed on the engine-man's stand. This
tube, on leaving the compartment of the chimney,
was protected against the effects of the external
refrigeration of the air, by a thick covering of hemp
carefully put on and defended by a coat of paint.
The receiver into which the steam was conducted
was 1 2 inches high and 3 inches in diameter. It bore
three instruments adapted to measure the pressure,
viz., an air-gauge, a thermometer, and a little
syphon-manometer. The syphon-manometer had
the inconvenience of filling with water, and was in
consequence abandoned ; but during all the obser-
vations which were made with the three instruments
their indications accorded exactly. Only, after the
stoppages of the engine, the thermometer-gauge was
much longer than the other two in marking the
pressure.
The whole of this apparatus is seen represented
in fig. 24 (PL V). VV is the tuhe which brings
PRESSURE IN THE BLAST-PIPE. 185
the steam from the blast-pipe to the receiver; A
is the receiver, closed at its upper part by a safety-
valve maintained in its place by the pressure of an
ordinary spring-balance F ; B is the air-gauge, and
r is the cock by which the steam arrived from the
interior of the receiver to the ball of the instrument.
C is the thermometer or thermometer-gauge ; dd is
the tube which conducted the steam from the re-
ceiver to the little syphon-manometer, which could
not be figured for want of room. In fine, the dis-
charging cock R, seen at the bottom of the receiver,
served to let out the water which formed therein by
condensation at the commencement of the experi-
ments and till the mass of the system had acquired
a proper temperature. The apparatus once suffici-
ently heated, this cock, when opened, let out no-
thing but a jet of perfectly transpareilt steam, and
never any water, which proved that no condensa-
tion of steam was taking place in the receiver.
The steam was taken at the point where the pipes
proceeding from each cylinder unite to form the
origin of the blast-pipe. At tins point the pressure
was successively that of the two cylinders. . Conse-
quently the rapidity of the alternations of the pistons
maintained there a mean constant pressure, at least
as long as no variation occurred in the circum-
stances which we shall presently speak of At the
moment of the starting of the engine, when the
velocity was but 2 or 3 miles per hour, the mercury,
at every stroke of the piston, was seen to rise sud-
186 CHAPTER VII.
denly, in the air*gauge and in the syphon-mano-
meter, to a height corresponding to about lfl>. of
effective pressure per square inch. But this effect
was produced and destroyed instantaneously, so that
in the duration of one stroke, the space of time
wherein the pressure was null was greater than that
in which it was lib. above the atmospheric pres-
sure. Afterwards, as the velocity of the eneine
increased, the mercury rose permanenUy in the
manometers, and its oscillations of level became
less and less sensible. At the velocity of 16 to 18
miles an hour a very sUght motion was still dis-
cernible in the surface of the mercury at every
stroke of the piston; but beyond that point the
oscillations became insensible, and the pressure
was no longer seen to vary but with the circum-
stances which formed the object of the experi-
ments.
The apparatus being fixed on the engine, when,
during the motion, the orifice of the blast-pipe was
contracted, it immediately caused the pressure to
rise in the manometers several pounds, according
to the contraction made in the aperture, and on
bringing back the blast-pipe to its former dimen-
sions the pressure returned to the same point as
before. Similarly, as the velocity of the engine
increased or diminished, the pressure in the blast-
pipe was seen to vary in a corresponding manner.
And finally, whenever, by putting coke on the fire
or water in the boiler, the vaporization of the boiler
PRESSURE IN THE BLAST-PIPE. 187
was temporarily diminished, the pressure in the
blast-pipe was instantly seen to lower, and to re-
sume its former degree only when the vaporization
had resumed its ordinary activity. There remained
no doubt then that the velocity of the engine, the
rate of vaporization, and the orifice of efflux of the
steam, had an immediate effect on the pressure in
the blast-pipe. As to the pressure in the boiler,
since the steam, before arriving at the blast-pipe,
passed first through the cylinder, it is clear that
the pressure in the boiler could not have modified
the pressure in the blast-pipe, but by first modi-
fying that of the cylinder. Now we shall here-
after show that this latter effect, from the boiler
to the cylinder, does not exist ; neither then could
it exist fix>m the boiler to the blast-pipe. And, in
fact, we observed that the augmentation of pressure
in the boiler was, according to the circumstances,
attended at times with an elevation, at other times
with a diminution of pressure in the blast-pipe, as
may besides have been remarked already in the
experiments related in Section vi. Chapter II.
Of the three circumstances just mentioned, as
modifying the effects of the blast-pipe, the first that
we chose to submit to inquiry was the influence of
the velocity of the engine on the pressure due to the
blast-pipe. For this purpose, the fire being kept in
the same state of intensity, and the boiler regularly
fed with water, in order to preserve, as much as
possible, a uniform vaporization, and the orifice of
188 CUAPTEB VII.
the blast-pipe being maintained constant, we made
the observations related in the following Table. We
thereto add the last column, in which is inscribed
the pressure which should have been observed, had
the variation taken place exactly in proportion to
the velocity.
To perform this calculation, we take as our point
of departure, in each series of experiments, the pres-
sure corresponding to the mean velocity of the
motion.
We must, however, add here, that nothing is
more difficult to obtain than uniformity in the va-
porization of the engine. Every time that coke is
thrown into the fire-box or water sent to the boiler,
the production of steam is immediately reduced,
though the velocity of the engine does not detect
the change, on account of its acquired impulse ; but
the difierence of vaporization is felt immediately in
the receiver, where, as has been said, the manome-
ters are seen to lower all at once and not to resume
their usual degree till after a certain time. A con-
trary effect takes place when the supply of the fire
and feeding of the boiler are momentarily suspended,
which especially happens during ascents, because the
engine-men are then apprehensive of diminishing the
power of the engine too much. These circumstances
oblige us, as the Table shows, to recur to the mean
of the observations, in order to obtain the corre-
sponding pressures and velocities.
We must equally give notice that in the two
PRESSURE IN THE BLAST-PIPE.
189
series of experiments contained in the Table, the
orifice of the blast-pipe was not the same.
Experiments to determine the inflttence of the velocity of
the motion, on thepresstare due to tJte blast-pipe.
Observed effec-
Effective pres-
sure calcu-
Velocity of
the engine in
miles per
hour.
tive pressure, on
the opposite face
of the piston, in
lbs. per sq. inch.
Mean
velocity.
Mean effective
pressure, by
observation.
lated, in the
direct ratio of
the velocity
of the motion.
15-
15-24
4- 1
4-4 /
1512
4-2
4-3
16-56
4-9
16-55
4-9
4-7
16-95
17-21
4-3 1
5-6 /
17-08
4-9
4-8
7-28
1-8
6-26
1-8
2-2
9-11
2-8
8-57
2-8
2-8
14-53
4-4
14-53
4-4
4-5
16-39
5-3 1
16-67
5-8 >
16-67
6-3
6-2
16-96
4-8 ,
17-50
17-73
5-1 1
6-2 /
17-61
5-6
5-5
We see by these results, that the eflFective pres-
sure exerted against the piston, by the action of the
blast-pipe, varies very nearly in the direct ratio of
the velocity of the piston, or of the engine.
From the considerations which we have presented
above, it still remained to seek according to what
law the pressure on the piston, in the action of the
blast-pipe, varies with the ratio of the vaporization
in the boiler, to the area of the blast-pipe through
which the steam is forced to flow. With this view
190 CHAPTER VII.
were undertaken the experiments which we shall
presently offer, note being carefully taken in them,
of the velocity of the engine, of the area of the blast-
pipe, and finally of the vaporization of the boiler.
After having compared the observations among
themselves, we find that the law to which they
approach nearest is that of a simple proportionality
to the ratio — , in which S' represents the total
0
vaporization or the expenditure of water of the
boiler, such as we observed it in the experiments,
and 0 represents the area of the orifice of the blast-
pipe. It is for this reason that we annex to the
Table of the experiments, a last column containing
the resistance against the piston created by the
blast-pipe, such as calculation would give it, sup-
posing that it were directly proportional to the
velocity of the engine, and to the ratio of the total
vaporization to the area of the blast-pipe, that is to
say, supposing it to be of the form
0
To obtain the coefficient K, which should serve to
operate this reduction, we first compared the pro-
s'
duct V — to each of the results given by observation,
and thence deduced the value of K, which was
found to be '0113. Consequently we calculate the
last column bv the formula
PRESSURE IN THE BLAST-PIPE. 191
•0113 t;—.
0
With regard to the observations of velocity and
pressure inserted in the Table which we are about
to present, we must notice that each of them is a
mean taken on from ten to twenty consecutive ob-
servations, which by so much the more insures their
accuracy. Nevertheless, as these observations were
all made at the same period of the experiment, and
at very short intervals of time from each other, it is
still found, on looking over the results to discover
the law which represents them, that the difficulty
already mentioned, of maintaining the imiformity of
the vaporization in the boiler, occasions from time
to time anomalies not inconsiderable in the observa-
tions. But on recurring to a mean taken between
observations made at two different periods of the
experiments, those anomalies are found to disappear
almost entirely ; which is a proof that they arise
solely from this, that the observed pressure in the
blast-pipe results from the momentary vaporization
of the engine, animated or slackened during that
portion of the experiment, whereas the calculated
pressure can be grounded only on the mean vapori-
zation of the whole experiment.
The observations we have just made are relative
to the last two columns of the Table. In that which
contains the dimensions of the blast-pipe, instead of
giving those dimensions in square inches, as re-
sulted from the form of the blast-pipe employed,
192 CHAPTER VII.
we give the diameter of a round blast-pipe offering
the same area of orifice. As the circular form is
the only one in use, we thought that the Table pre-
sented in this manner, would become more commo-
dious for practical appUcations.
Finally, we must yet add, that in the experiments
about to be related, we have sometimes reduced the
area of the orifice of the blast-pipe to but 2*50 and
3*125 square inches, and thence resulted, even for
very moderate velocities, very great resistances
against the piston. But such contractions are not
in use: before the variable orifice which we have
described was fitted up on the Star engine, the
blast-pipe was of the diameter of 2f inches, or 4*5
square inches of area, which is a measure usual
enough in these engines. The blast-pipe then, in
the regular use of it, produces only resistances
proportioned to that dimension; and this remark
is necessary, that the results related in the Table
may not be r^i^rded as mean data suitable to the
regular work of locomotives.
\
PRESSURE IN THE BLAST-PIPE.
193
Experiments on the resistance produced against the piston by
the action of the blast-pipe.
Vapatintion
Effeetire pres-
EfliBCtiTe pras-
daring the
rareagamat
sure, ealca-
Bxperiment, in
Velodtjrof
the piston,
latedbythe
Dtte of the experiment, ead
cubic feet (tf
Diameter
theensine,
innulea
obeerred du-
fonnuhi
dedgnetmi of the eneine
and its loed, tender indnded.
water per
of the
ring the
experiment.
8'
• Jftl ft 4k .a* ^^
hour.
bbMt-pipe.
per hoar.
0113 0 _.
e
1836.
cuhic feet
inches.
miles.
lbs.persq.in.
tbs.persq.in.
Aug. 9, Star, from LiTer-
pool to Manchester, with
120*27 tons . . . .
67-71
1-995
16-95
4-3
4-1
15-00
15-00
5-01 .
3-0 J*
3-6/ *
17-21
5-6
4-2
15-24
4-4
3-7
Aug. 9, Star, from Man-
16-55
4*9
4*0
chester to Liverpool,
with 75-05 font . .
68-79
1-995
16-96
4*8
4*2
*
17-50
5-1
4-3
14-53
4-4
3-6
16-67
5-8
4-1
16-39
5-3
4-1
17-73
6-2
4-4
Aug. 9, 5'/ar,with 38*58 «»•.
68-79
1-995
911
2-8
2-3
Aug. 9, 5/flr,with 4 1 -9 7 «".
68-79
1-995
7-28
1-8
1-8
Aiig.9,Slfar, from liverp*.
to Manch'. with 96*30 *».
60-64
2-821
22-85
3-0
2*4
*
20-00
2-4
2-1
20-00
2-3
2-1
21-82
1-8
2-3
17-56
2-3
1-9
Aug. 10, Star, from Li-
19-25
2-0
21
verpool to Manchester,
with 43-65 tons . . .
65-49
2-360
23-64
2000
2-4 r®
4-01
3-4,
3-7
26-67
25-00
*'^l3-7
1-8/^^
4-51
4-2
4-3
20-69
2-9
3-5
Aug. 13, Star, from Li-
20-77
2-2
3-5
verpool to Manchester,
with 109-68 tons . .
54-20
2-360
19-57
1-0
2-7
1-995
13*33
2-4
2-6
1714
3-8
3-4
10-29
2-1
2-0
12-63
1-6
2-5
Aug. 13, Star, from Man-
12-47
1-2
2-5
chester to Liverpool,
with 48-48 tons . .
62-83
1-784
21-82
5-4
6-2
23-53
5-0
6-7
18-75
4-2
5-3
19-20
3-4
5-5
2000
\IV^
5-7
2000
5-7
194 CHAPTER VII.
Comparing the last column and the last but one
of this Table, we recognise between them a suffi-
cient coincidence for practical purposes. Conse-
quently, in all cases wherein the resistance caused
against the piston by the action of the blast-pipe
shall not have been directly observed, it may be
determined by the formula
•0113 v—;
0
in which v is the velocity of the engine in miles per
hour ; S' the total vaporization of the boiler in cubic
feet of water per hour ; o the area of the orifice of
the blast-pipe expressed in square inches ; and the
result of the calculation will give the pressure in the
blast-pipe expressed in pounds per square inch.
The pressure per square foot will be 144 times as
much.
With respect to the quantity represented here by
S^ the experiment from which we deduced the
formula shows, that the vaporization signified is
the total vaporization effected in the boiler, that
is to say, the vaporization counted before deduction
of the water carried away in a liquid state with the
steam. But as the engine Star makes habitually
no waste of steam by the safety-valves, it is un-
derstood that in engines in which this loss does
take place, it is not considered as included in the
value of S', and consequently, if a very nice accu-
racy be desired, it will be proper, first of all, to
PRESSURE IN THE BLAST-PIPE. 195
subtract it from the vaporization effected, in order
to obtain the quantity here expressed by S^
Making in the preceding formula
•0113— = /,
the pressure in the blast-pipe may be represented by
the expression
p V,
in which p^ will be the ratio of the vaporization to
the orifice of the blast-pipe, multiplied by a constant
coefficient.
Now, for engines which vaporize as much as 60
cubic feet of water per hour, practice has established
the use of a blast-pipe of 2*25 inches diameter, or
3*96 square inches of area, which gives for the value
S'
of the ratio — ,
0
= 15-2
396
In constructing engines of a greater vaporizing
power, it would be natural to increase the area of
the blast-pipe in proportion to the quantity of steam
to which it is to give issue. There is room therefore
to think that the proportion thus established be-
tween the production of steam and the area of the
blast-pipe, will not be notably changed by the dif-
ferent engine-makers. Consequently the ratio —
may be regarded approximatively as a constant
quantity, given by the above proportion.
196 CHAPTER VII.
Then the preceding formula will be reduced
simply to the expression
•175 r,
which will be useful especially in valuing the pres-
sure due to the blast-pipe in engines whose vapo-
rization is unknown. In this formula, t; is the
velocity of the engine, in miles per hour, and the
result is the pressure in the blast-pipe, expressed in
pounds per square inch. As the pressure per square
foot is 144 times as much, it follows that if we
require the pressure expressed in that manner, as
will be found necessary in the course of this work,
we shall obtain its value by the formula
25-2 v.
We shall then represent generally the pressure in
the blast-pipe under the form
and for the most ordinary cases, it will suffice to
give to f\ in this expression, one of the constant
values above mentioned, according to the measures
employed. But if the engine in question should
differ too considerably from the proportions which
we have just indicated with reference to the area of
the blast-pipe, it would be necessary to substitute
for that approximate value of j?^ its value function
of S' and o.
In fine, to dispense with all calculation on this
head, we here subjoin a Table, in which will be
found, on inspection, the pressures in the blast-pipe
T
PRESSURE IN THE BLAST-PIPE. 197
for given circumstances, and we continue that Table
beyond the actual effects of locomotive engines. It
will there be recognised how, by augmenting the
orifice of the blast-pipe, the resistance against the
piston, arising from that cause, may be diminished
at pleasure ; and it may probably be found, in con-
sequence, that in the regular work of locomotives, it
might be useful to adopt a blast-pipe with a variable
orifice, such as we employed temporarily in our
experiments. Then, by contracting the orifice of
efflux of the steam only just as much as is necessary,
there will be no more resistance against the piston
than what is indispensable for the proper action of
the engine.
I
f
198
CHAPTER VII.
Practical Table of the pressures against the piston, due to
the action of the blast-pipe.
Diame-
ter of the
blaat-pipe.
VdocitT
of the
engine,
in miles
per hoar.
EffiBcthe pcessure aninst the piston, in lbs. per square inch, the
T^wnaatton of the Dotler, in cubic feet of water per hour, being:
30
40
50
60
70
80
90
100
S inches.
miles.
6
10
15
90
S5
SO
85
40
Ifaa.
0*5
1-1
1-6
S'S
S7
3*9
3-8
48
ft*.
07
1-4
9-9
99
80
4*3
5*0
5*8
lbs.
0*9
1*8
9*7
30
4-5
5*4
OS
7-9
lbs.
ri
9*9
3*9
4*8
5*4
0*5
7-0
8*0
tbs.
1*3
9*5
8*8
5*0
OS
7*0
8*8
10*1
tbs.
t>
»>
>t
>t
If
tt
tbs.
It
II
II
11
II
»l
II
II
lbs.
f*
II
f>
It
It
If
tt
It
Siinchea.
5
10
15
SO
S5
SO
35
40
0'4
0-9
1*3
17
9-1
90
3-0
3*4
00
1-1
17
9*3
9*8
3*4
4*0
4*5
07
1*4
9*1
9*8
3*0
4*3
50
57
0*9
17
9*0
3*4
4*3
5'1
0*0
0*8
1*0
9*0
8*0
4*0
5*0
0*0
7*0
8*0
1*1
9*8
3*4
4*5
0*8
8*0
9*1
It
II
11
II
II
II
It
II
>l
ft
It
•1
It
tt
tl
n
Si inches.
5
10
15
90
95
SO
35
40
45
50
0*3
07
10
1-4
17
9-1
9-4
9*8
8'1
3-5
0-5
0-9
1-4
1-8
9-3
9*8
3*9
37
4*1
40
0*0
1*9
17
9*9
9*9
8*5
4*0
4*6
5*9
5*8
07
1*4
9*1
9*8
3*5
4*1
4*8
5*5
0*9
0*9
0*8
1*0
9*4
8*9
4*0
4-8
5*0
0*4
7*3
8*1
0*9
1*8
9*8
3*7
40
5*5
0*4
7*4
8*3
9-9
ro
9*1
3*1
4.1
5*9
0*9
7*8
8*3
9*3
10*4
11
tt
tl
•I
1 ::
It
tl
It
9f inches.
5
10
15
90
95
80
35
40
45
50
0*3
0-0
0*9
VI
1*4
17
9-0
9-3
90
9*9
0*4
0-8
1-1
1*5
1-9
9*8
9*7
8*0
3*4
3*8
0*5
1*0
1*4
1-9
9*4
9*9
8-3
3*8
4*3
4*8
00
1*1
17
9*3
9*9
3*4
4*0
4*0
5*1
57
07
1*3
9*0
97
8*3
4*0
4*7
5*3
0*0
0*7
0*8
1*5
9*8
3*0
3*8
4*0
6*8
0*1
0-8
70
0*9
17
9*0
3*4
4*3
5*1
0*0
0*8
77
8*0
10
1-9
9*9
S-8
4*8
£•7
0-7
7*6
8*0
9-5
3 inches.
5
10
15
SO
95
30
85
40
45
50
55
00
0*9
0*5
07
I'O
1*9
1-4
17
1-9
9-9
9-4
9-0
9-9
0*8
00
1*0
1*3
10
1-9
9*9
9*0
9*9
8*9
3*5
3*8
0*4
0*8
1*9
1*0
9*0
9*4
9*8
3*9
3*0
4*0
4*4
4*8
0*5
1*0
1-4
1-9
9*4
9*9
3*4
3*8
4*8
4*8
5*3
5*8
O'O
1*1
17
9*9
9*8
3*4
3*9
4*5
5*0
5*0
0*9
0*7
O'O
1*3
1*9
90
3*9
3*8
4*5
5*1
5*8
0*4
7*0
77
07
1*4
9*9
9*9
3*0
4*8
5*0
6*8
0*5
7*9
7*9
8*0
0-8
1*0
9*4
3-9
4*0
4-8
50
0*4
7-9
8*0
8-8
9*0
3i inches.
5
10
15
90
S5
80
85
40
46
50
55
60
0-9
0*4
0*0
0*8
ro
1'9
1-4
l-fl
1*8
9*0
9-9
9-4
0-3
0*5
0*8
1*1
1*4
1*0
1-9
9*9
9*4
97
8*0
3*9
0*3
07
1*0
1*4
17
9*0
9*4
9*7
3*1
3*4
3-7
41
0*4
0*8
1*9
1*0
9*1
9*5
9*9
3*3
37
4*1
4*5
4*9
0*5
1*0
1*4
!•»
9*4
9*9
3*3
3-8
4*3
4*8
5*9
5*7
0*5
1*1
1*0
9*9
9*7
8*3
3*8
4*4
4-9
5-4
6*0
0*5
0*0
1*9
1*8
9*4
8*1
3*7
4*8
4*9
5-5
0*1
0*7 1
7*3 1
07
1*4
9*0
9*7
3*4
41
4*8
5-4
0*1
0*8
7*5
8*9
I
L
PRESSUBE IN THE BLAST-PIPE.
199
Velocity
EfliectiTe pressure aominst the piston, in tbs. per square inch, the
Diameter
of the
blaat-pipe.
of the
engine,
in miles
per hoar.
▼aporisabon of the boiler,
in cubic feet of water per hour, be
sing:
100
30
40
50
60
70
80
90
mOes.
lbs.
lbs.
lbs.
lbs.
lbs.
lbs.
lbs.
lbs.
34 Indies.
6
O'S
0*9
0*3
0*4
0*4
0*5
0*5
0*6
10
0-4
0-5
0'6
07
0-8
0*9
VI
1*9
15
0*5
07
0*9
1*1
1*9
1*4
1-6
1*8
90
07
0*9
1-9
1*4
1*6
1-9
9*1
9*3
S5
0*9
1*9
1*5
1'8
91
9-4
9-7
9*9
30
I'l
1-4
17
9*1
9*5
3*8
3*9
3*5
35
1-2
1-6
9-0
9*5
9*9
3*3
37
4*1
40
1-4
1-9
S'3
9*8
3*3
3*8
4*9
47
45
1-6
9-1
9-6
3*9
3'7
4-9
4*8
5-3
50
1-8
9-4
9-9
3*5
4-1
47
5*3
8*9
55
19
9-6
3-9
8-9
4*5
5*9
5*8
6-5
60
9*1
9-8
3-5
4-9
4'9
5-6
6-4
70
3f inches.
5
0-2
0'9
0-3
O'S
0*4
0*4
0-5
0*5
10
0-3
0-4
0-5
0*6
07
0*8
0*9
1*0
15
0*5
0*6
0-8
0-9
ri
1*9
1*4
1*5
20
0*6
0*8
ro
1*9
1-4
1*6
1*8
9*0
S5
0*8
I'O
1-3
1*5
1*8
9*1
9*3
9-6
90
O'Q
1-9
1*5
1-8
9*1
9*5
9*8
3*1
85
l-l
1-4
1-8
9*1
9*5
3*9
3*9
3*6
40
1*9
1-6
90
9*5
9-9
3*3
3*7
41
45
14
1-8
9*3
9*8
3*9
3-7
4*1
4-6
50
1*5
9-1
9*6
3-1
3-6
4-1
4*6
5*1
55
17
9'3
9*8
3-4
3*9
4*5
6*1
5*6
60
1'8
9*5
3*1
37
4*3
4-9
5*5
6*1
4 inches.
5
O'l
0'9
0-9
0-3
0*3
0*4
0*4
0-5
10
O'S
0*4
0-5
0*5
0*6
0-7
0*8
0*9
15
0-4
0-5
07
0*8
0*9
I'l
1*9
1-4
SO
0-5
07
0-9
1*1
1-3
1*4
1*6
1*8
S5
07
0*9
l-l
1*4
1*6
1*8
9*0
9*3
30
0*8
1-1
1*4
1-6
1-9
9-9
9*4
9*7
35
0*9
1*3
1-6
1-9
9-9
9-5
9*8
3*2
40
1-1
1*4
1-8
9-9
9-5
9-9
3*9
3*6
45
1*9
1-6
90
9-4
9*8
3*9
3-6
4*1
50
1*4
1-8
9-3
97
3*9
3*6
4*1
4-5
55
1-5
90
9'5
3-0
3*5
4*0
4-5
50
60
1-6
9*9
97
3*9
3*8
4'3
4*9
5-4
CHAPTER VIII.
OF THE FRICTION OF LOCOMOTIVE ENGINES.
ARTICLE I.
OF THB FRICTION OF UNLOADED LOCOMOTIVE
ENGINES.
Sect. I. Of the divers elements of the friction of
locomotive engines.
After having examined the resistance offered by
the loads to be moved, it will be proper also to
make known the passive resistance or friction of the
movers which we have to employ ; for it is only the
surplus of their power over and above what is
necessary to propel themselves, that these movers
can apply to the drawing of burdens.
While a locomotive engine is performing the
traction of a train, it evidently requires: — 1st, a
certain force to make the train advance, or to over-
come the resistance of all the loaded carriages ; and
2dly, another force to propel itself by overcoming
its own friction. It is this second force, that which
causes the engine to move, which represents the
FRICTION OF UNLOADED ENGINES. 201
friction of the engine ; whereas the first is the resist-
ance of the load^ and the union of the two efforts
constitutes the total force applied by the mover.
The friction of a locomotive engine is then the
force it expends to maintain itself in motion on the
rails. But that force must clearly vary according
to the weight or resistance of the load which the
engine draws. In effect, the greater that weight,
the greater also will be the pressure it causes on the
axes of rotation, and on the divers moving parts of
the apparatus ; and as the friction is always in pro-
portion to the pressure, it follows that the friction
which takes place at these points, must augment with
the load. Hence the friction of the engine, which
is nothing more than the force resulting from the
union of these different frictions, must equally
increase with the load.
Thus, we shall first establish a difference between
the friction of an engine unloaded^ and that of the
same engine loaded.
On the other hand, the force requisite to set in
motion an unloaded engine may itself be decomposed
into two portions arising from two distinct causes :
Ist, that which is necessary to overcome the friction
of all the parts of the apparatus itself, and which
would be observed if the engine were supported on
its axles and did not propel its own weight along the
rails ; and 2dly, that which is necessary to execute
the progressive motion, that is, to overcome the
202 CHAPTER VIII.
particular friction caused on the axles and wheels
by the weight of the engine, as in other carriages.
Finally, then, we will consider the fiiction of a
locomotive engine, under any circumstances what-
ever, as composed of the three following resistances :
1st. The resistance due to the friction of its
mechanical organs.
2d. The resistance arising from the weight of the
engine, considered as a carriage.
3d. The additional friction, caused in the engine,
by the load it draws.
If we knew these three elements of the total
resistance separately, it is plain that we could,
under all circumstances, conclude from them the
friction of a locomotive engine whose construction,
weight and load, were known. These must then be
the present object of our inquiry.
To attain our end, we shall first seek to determine
the friction of unloaded engines, which is the sum
of the two first of the resistances mentioned above ;
and deducting from this the resistance of the engine
considered as a carriage, which may easily be done,
since in this respect the engines may be assimilated
to waggons, we shall obtain the friction of the me-
chanical organs of the engine. Thence we shall
pass to the second part of our inquiry, which will
consist in determining the additional friction of the
engines, according to the load they draw.
FRICTION OF UNLOADED ENGINES. 203
Sect. II. Of the different modes of determining the
friction of unloaded engines.
The force necessary to move an unloaded loco-
motive engine may differ according to two different
circumstances :
1st. The steam remaining shut in the boiler, and
having no access to the mechanism nor exerting
any pressure on it, so that the progression of the
engine be produced by an external agent.
2nd. The steam being the agent which produces
the motion.
The difference between these two cases cannot
be very great ; for in both circumstances the load
of the engine remains the same, being no other
than its own weight. Besides, whatever be the
means that make it move, it goes forward; thus
at each turn of the wheel there is a complete
revolution, and therefore a complete friction, of
all the mechanism. The steam, in order to move
the engine, would have applied a certain force.
That force would have produced pressure, and con-
sequently proportional friction, on all the points
compressed. Now, the moment we make the
engine advance, we apply a force equal to that
which the steam would have applied. Thus we
produce on all the joints the same pressure, and
consequently the same friction, as the force of the
steam would have produced. Of all these joints
\
204 CHAPTER VIII.
or moving parts, it is only those, therefore, whereon
the steam acts in a direct and particular manner,
which are not equaUy compressed in both cases.
These parts being strongly pressed one against the
other when the steam is admitted into the cyUnders,
cease to experience that pressure, and in conse-
quence have indisputably less friction, when the
steam takes no part in creating the motion. But
the parts on which the steam exerts a direct pres-
sure are merely the two slides.
The surface of the slide, on which the pressure of
the steam acts, is generally 7^ inches by 6, or 45
square inches; which makes 90 square inches for
the two slides. When we suppose the engine
moving alone, and without drawing any train after
it, we cannot suppose that the effective pressure
of the steam in the boiler need be more than
10 lbs. per square inch. We shall see by experi-
ment that it may be no more than 4 or 5 lbs. The
pressure made by the steam on the slides is then,
at most, 900 lbs. Taking the friction of iron
against iron, poUshed and lubricated with oil, at
^Q of the pressure, it would be a friction of 90 fbs.
But it is well known that a force appUed at one
point of an engine, when transmitted to another
point of the same engine, changes its intensity in
the inverse ratio of the velocity of the points con-
sidered. The slide moves but 3 inches at each
stroke of the piston, or ^ foot at each turn of the
wheel, that is to sav, it traverses but ^ a foot, while
FRICTION OF UNLOADED ENGINES. 205
the engine, having a wheel of 5 feet in diameter,
advances 15*71 feet. The friction of the slide,
therefore, considered as opposing the motion of
the engine, creates at most a definitive resistance
of ^^t 2^ — , ^ 1,1 or about 3 fts. Whence it is
2 X 1571
seen that in practice the friction determined, either
in the first case, or in the second, may be con-
sidered as the true friction of the engine when it
draws no load.
Sect. III. Fricton of the engines determined by the
smallest pressure of steam necessary to keep them
in motion.
The reflections developed above, and tending to
prove that the force necessary to move an engine is
sensibly the same, whether the power of the steam
itself be employed to set it in motion, or any
external agent be used, gave us three means of at-
taining the knowledge of the friction of the engines
when drawing no load. The first consisted in seek-
ing what was the least pressure of steam requisite
for a locomotive to maintain itself in motion on the
rails, when it had no more than its own friction to
overcome ; the second was the use of the dynamo-
meter ; and the third was the method of the angle
of friction, already employed with respect to wag-
gons. All three were tried successively.
20(5 CHAPTER VIII.
The principle on which the first of these methods
is founded is this : if the steam, exerting a known
effective pressure per square inch, or per unit of
surface of the piston, be found sufficient to keep
the engine in motion, at a velocity however small,
but yet at a uniform velocity, it follows that the
effort then developed is just sufficient to hold the
friction of the engine in equilibrio ; for if it were
greater, the velocity would increase, and were it
less, the velocity would diminish. In this case,
then, in order to obtain the measure of the friction,
it suffices to calculate the effort applied by the
engine, which is easy, since the area of the two
pistons is known, as well as the pressure exerted
by the steam per square inch of their surface.
It must only be observed, according to the prin-
ciple already mentioned, that the pressure exerted
on one part of an engine, on being tmnsmitted to
another part of the same engine, reduces itself in
the inverse proportion of the velocity of the points
of application. In the case before us, the velocity
of the engine is to that of the piston, as the circum-
ference of the wheel is to twice the stroke, since the
piston makes two strokes while the wheel performs
one turn. A force applied on the piston produces
then, for the progression of the engine, only a force
reduced in the inverse proportion of these velocities,
that is to say, as twice the stroke is to the circum-
ference of the wheel.
FRICTION OF UNLOADED ENGINES. 207
Let d be the diameter of the piston, ^ird^ will be
the area of one of the two pistons ; P-^p being the
effective pressure of the steam per unit of surface,
will be the effective pressure on both pistons. If,
moreover, / express the length of the stroke of the
piston, and D the diameter of the wheel, the effec-
tive force of translation resulting for the engine, in
virtue of this pressure, will be then
^ird^ (P -i>) X ^ or £' ,
which, from what has been said, will give the
measure of the friction of the engine.
It must be noted, that the pressure of the steam
in the cylinder is here taken as equal to that which
exists in the boiler. The reason of it is that, in
the experiments which we shall have to make by
that mode, the motion of the engines being always
extremely slow and the regulator entirely open, the
two pressures will have time to settle in equilibrio,
and therefore will be equal to each other.
To ascertain the smallest pressure capable of
moving the engine, it was necessary to take that
engine at a time when it was producing steam at
a very low degree of elasticity. The evening, after
the work was done, and the fire thrown out of the
fire-box, when the water in the boiler was beginning
to lose its heat, and the steam arising from it was
208 CHAPTER VIII.
gradually losing its force, was the moment favour-
able for trying the smallest pressure at which the
engines could move along the rails. The spring-
balance, which closed the safety-valve, showed the
pressure of the steam in the boiler, by loosening
the spring till it was precisely in equilibrio with
that pressure; and to make the observation more
sure, the engine was immediately brought to the
stationary syphon-manometer, and that instrument
gave the true pressure per square inch in the boiler
at the moment of the experiment. In this manner
were made the following experiments, of which we
shaU only give the first in detaU.
On the 5th July, 1834, the engine Atlas, cylin-
der 12 inches, stroke of the piston 16 inches, weight
11*40 tons, wheels 5 feet, 4 wheels coupled, was
submitted to the experiment separate from its
tender.
The spring of the balance being loosened more
and more, to show the pressure of the steam in the
boiler, as it gradually lowered, the following trials
were made.
At 2 lbs. of pressure marked on the balance, the
engine moved forwards and backwards, passing from
rest to motion, or surmounting, besides the friction,
what is called the vis inertue of the mass of the en-
gine ; that is to say, not only preserving an acquired
velocity, but acquiring it ; which proves an excess
in the moving power above the resistance.
At Ifb. of pressure similarly marked, the engine
\
FRICTION OF UNLOADED ENGINES. 209
started, passing again from the state of rest to that
of motion.
The pressure still lowering a little, and the balance
being at zero, the engine continued to move. At
this moment it was brought under the manometer.
The instrument marked 4 lbs. of effective pressure
per square inch in the boiler, the valve then bearing
merely the weight of the lever or something less,
which was not discernible on the balance, as the
lowest pressure it could indicate was that of the
lever.
The cyUnder being 12 inches in diameter, the
area of the two pistons was 226 square inches.
Thus a pressure of 4 tbs. per square inch produced
on the piston a force of 226x4=904 lbs., that is
to say, it could move a resistance of 904 lbs. at the
velocity of the piston. But at the velocity of the
engine, which is greater in the proportion of the
circumference of the wheel to twice the stroke, or
could overcome only a resistance of ^,g^^y' == 1 54
tbs.
Thus, as we have seen that the engine still moved
at the moment when it was put under the mano-
meter, though the pressure was then reduced to
4fi>s., it is plain that the resistance of the engine
did not exceed 1 54 lbs.
This first experiment had been made with the
J
210 CHAPTER VIII.
engine separate from its tender, with a view not to
entangle one resistance with another; hut wishing
to apply it to lighter engines with uncoupled wheels,
an inconvenience occurred. The pressure necessary
to move the engine alone without tender was sq low
that the spring-balance could not indicate it, that
pressure being less than the weight of the lever
itself. Another inconvenience of this low pressure
was, that it could not be obtained till the moment
when the boiler produced no steam at all ; so that
the pressure was then lowering so rapidly that the
accuracy of the experiment could not be de-
pended on.
But as the resistance of the tender-carriage might
easily be calculated from the experiments made on
the friction of the carriages already inserted above,
it was easy to take account of it. Thus the tender
being left attached to the engine, the experiments
offered the same degree of accuracy, with greater
facility in observing the pressure of the steam.
For this reason, in the following experiments the
tender-carriage was no longer separated from the
engine.
These experiments were made in a manner entirely
similar to the one we have just explained; save,
that to deduce from them the firiction proper to the
engine itself, we subtracted for the traction of the
tender, first 6 fts. per ton, and again 1 lb. per ton
for the additional friction which every ton of that
load produced in the engine, according to what will
FRICTION OF UNLOADED ENGINES. 211
be seen in the second article of this chapter. We
shall only, therefore, present in the following Table
the elements and the results of these experiments.
We have neglected the resistance due to the blast-
pipe, on account of the slowness of the motion, and
especially of the little vaporization which took place
in the boiler.
f
212
CHAPTER VIII.
i
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FRICTION OF UNLOADED ENGINES. 213
Sect. IV. Friction of the engines^ determined by the
dynamometer.
At the same time that the friction of the engines
was determined in this manner, other essays were
also made to obtain the valuation of that friction by
means of the dynamometer.
On the 22nd of July, the engine Vulcan, cyUnder
11 inches, stroke 16 inches, wheels 5 feet, weight
8*34 tons, one pair of wheels only worked by the
piston, being ready to start for Manchester, its
boiler full of water, and fire-box full of coke, was
separated from its tender. A circular spring-balance
was fixed to the engine, and a lever passed through
the ring of the balance, for two men to draw the
engine by means of the lever.
The engine was first set in motion by five or six
men. As soon as the first impulse was given, the
two men at the -lever kept it in motion without
difficulty at the velocity of between 2 and 3 miles
per hour. The style of the balance oscillated
considerably; it went generally from 130 fts. to
170 lbs., giving a mean traction of 150Sbs.
The balance was then taken off the front of the
engine and fixed on the hinder part, then turned
towards Liverpool, and the same experiment re-
newed gave a mean traction of 140 fts. The style
still oscillated, in general, some twenty pounds above
and below that point.
Mean of these two experiments 145 lbs.
214
CHAPTER VIII.
The engine was ready to start, and had akeady
taken a few runs on the rails to get up the fire and
fill the boiler. Thus the greases which served to
lubricate the rubbing parts were melted, and the
oils quite liquid. But the experiments being made
within the enclosure of the station, on a place of
continual thoroughfare, where the rails are con-
stantly covered with cinders and dirt, this circum-
stance must have greatly augmented the resistance
to the motion.
We here subjoin the Table of three other ex-
periments, made in a similar manner.
Experiments on the friction of unloaded locomotive engines j
by the dynamometer.
Number
of the
experi-
ment.
Dmteoftbe
experiment.
Name of
the engine.
j
Diune- - Stroke
terofthe of the
cylinder.' piiton.
Diame-
ter of the
wheel.
Weiffht
of the
engine.
Friction
of the
engine.
inches, inches.
feet.
tons.
lbs.
VI.
July 22, 1834.
Vulcan.
11
16
5
8-34
145
VIL
July 23, 1834.
Sun.
11
16
5
7-91
115
VIII.
Do.
FiBXFLT.
11
18
5
8-74
127
IX.
Do.
Fury.
11
16
5
8*20
105
Sect. V. Friction of the engines^ determined by the
angle of friction.
The results obtained by the dynamometer were
not very far different from those obtained by the
least pressure ; but as in all these experiments, the
FRICTION OF UNLOADED ENGINES. 215
style of the balance oscillated exceedingly, in con-
sequence of the little inequalities of the way, or the
jerks given by the men who drew the engine, it
was very difficult to ascertain the mean traction.
It was very desirable, therefore, to determine the
friction of the engines by a different method, in
which that cause of error should not exist.
For this reason the engines were submitted to the
same experiments that had served to determine the
friction of the waggons.
These experiments having been made and calcu-
lated exactly like those on the waggons, we shall
merely give their results in the following Table.
Account was taken of the resistance of the air
against the wheels, in the same manner as in the
experiments on the friction of waggons.
216
CHAPTER VIII
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FRICTION OF UNLOADED ENGINES. 217
Sect. VI. Table of the results of the preceding ex-
periments on the friction of unloaded engines.
Finally, for the convenience of making researches,
we unite the results of these different experiments
in one Table.
218
CHAPTER VIII.
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FRICTION OF UNLOADED ENGINES. 219
In all these experiments we find that those made
on the inclined plane give less friction than those
made in the enclosure of the station, whether hy the
dynamometer or hy the least pressure. This result
has already been explained by the sand, cinders, or
mud, which alwajrs cover the rails at the station ;
but, on the other hand, in the experiments made on
the inclined planes, if the regulator of the engine
did not close the passage hermetically, a slight
escape of steam may have taken place in the cy-
linders, and in a certain degree favoured the motion
of the engine. The results then of the two modes
of experiment deviate contrary ways, and the dif-
ference between them not being very considerable,
we have reason to think that their mean gives the
result required with an accuracy sufficient for
practice.
Examining these experiments, to deduce from
them a general datum, and leaving out the engine
Vesta, which was found to be in an exceptional
case, we perceive that engines such as the Sun,
Firefly, Vulcan, Fury, Leeds, and Jupiter, of
an average weight of 8 tons, and with four wheels
not coupled, have a mean friction of 104 lbs.
That the engine Atlas, of the weight of 1 1 tons,
having six wheels, four only of which are conical
and with flanges, but coupled, has a friction of
139 lbs.
And finally, that the engine Star, of the weight
220 CHAPTER VIII.
of 1 1 tons, with six flanged wheels, has a friction of
176 fts.
We shall presently see that these differences de-
pend in part on the weight of the engines. But it
will readily be conceived that the friction being
influenced by so many different circumstances, it is
impossible to imagine that it can be identically the
same, not merely in engines of a different con-
struction, but even in engines perfectly similar to
each other, and coming from the very same builders.
The observed differences ought not then to surprise.
Sect. VII . Of the friction of the mechanical organs
of the engine^ and of its friction as a carriage.
In the preceding paragraphs we have determined
the friction of unloaded engines ; but we have
already said that this friction is composed of two
parts, viz., the resistance arising from the weight
itself of the engine, considered as a heavy carriage
to be drawn along the rails ; and that which results
from the friction of the different parts of the me-
chanism, and which would equally take place if the
progressive motion did not exist. As the first of
these two forces varies with the weight of the
engine, and as the second, on the contrary, is
nearly constant for engines of the same proportions,
it will be proper now to estimate them severally in
the total friction of the unloaded engine.
FRICTION OF UNLOADED ENGINES. 221
We have seen above that locomotives such as
SuN^ Firefly, Vulcan, Fury, Leeds, and Ju-
piter, have a mean friction of 104 lbs. In the
state m which those engines were submitted to ex-
periment, their load was their own weight. Now we
know that a weight of 1 ton, carried on waggons
with springs as we have described, opposes to the
traction on a railway a resistance of 6fts., and we
shall presently see that the effort of this traction
creates, moreover, in the engine, an additional fric-
tion of 162 X 6 lbs. = 97 ft. ; which makes in all
7 fts. per ton. On the other hand, the engines,
considered as carriages, are of a construction quite
similar to that of the waggons. The wheels and
axle-trees have not indeed the same dimensions in
both cases. In the engines, the axle-bearings are
somewhat thicker in proportion to the diameter of
the wheels, which is disadvantageous as to the
friction on the axle, but the difference is trifling;
and again, the wheels of the engines being larger,
offer somewhat less resistance as to the friction of
rolling. Besides, they are greased, and kept with
* more care. We may therefore, without any im-
portant error, assimilate the engines to waggons
with reference to their friction as carriages. Then
it will be easy to deduce from the total friction of
the engine the portion attributable to its weight,
and the remainder will be the friction of the ma-
chinery. The engines which have just occupied
our attention, and whose friction is 104 fts., ai;e of
i
222 CHAPTER VIII.
the average weight of 8 tons ; they create then, as
carriages, a total resistance of 56 lbs., and conse-
quently the friction of their mechanical organs
amounts to 48fts.
As to the Atlas engine, the passive resistance of
which is 139 fts., the same calculation makes the
friction of the mechanical organs amount to 59 fts. ;
and there is room to think that the excess of this
number above the preceding depends on the coupling
of the wheels of the engine.
With respect to the engine Star, we can draw no
conclusion, for want of knowing precisely the fric-
tion of a carriage borne on six flanged wheels, as
that engine is.
These calculations authorise us then to consider
the resistance of the mechanical organs in engines
of the kind described above, and when in good
order, as being at a medium from 48 to 59fts.
Consequently, to value in pounds the friction of
an unloaded locomotive engine, the number 48, or
the number 59, which, according as the engine has
its wheels unconnected or coupled, represents the
friction of its mechanical organs, must be added to
its total friction as a carriage, which is no other
than the product of its weight expressed in tons by
the number 7.
The same result will be attained approximatively
by simply taking the friction of the engines at 1 5 lbs.
per ton of their weight, that is, at twice and a half
the friction of the waggons.
ADDITIONAL FRICTION OF THE ENGINES. 223
This manner of estimating the (riction of the
engines is useful whenever it is wished to calculate
the effect that may be expected finom them, without
having recourse to an immediate experiment. But
it is espedaUy necessary, when, before constructing
a locomotive, it is required to determine the pro-
portions it ought to have in order to produce desired
effects. In this case, indeed, the calculation cannot
be performed without emplo3ring in it the presumed
friction of the engine, and as the weight intended
for the engine is always decided previously, it will
be easy to derive the friction it will have, if it be
properly constructed.
ARTICLE II.
OF THE ADDITIONAL FRICTION OF LOADED LOCO-
MOTIVE ENGINES.
Sect. I. Of the mode of determination.
We have just determined the friction of loco-
motive engines when they draw no load but their
own weight. But those engines are never employed
in that way, and we have shown that the friction of
the same engine must become greater as it draws a
greater weight ; because the augmentation of weight
increases the pressure exerted on the different
moving parts of the apparatus, and with the pres-
sure increases necessarily also the corresponding
friction. We shall now, therefore, endeavour to
224 CHAPTER VIII.
determine the precise value of this surplus of re-
sLstance produced in the engine by virtue of the
load which it draws.
When an engine performs the traction of a train,
the pressure of the steam in the boiler is known
finom inspection of the manometer or of the balance
of the safety-valve. But the pressure of that steam
in the cylinder is not known, because in passing
from the boiler to the cylinder it alters its elastic
force, as will be seen further on. If the pressure in
the cylinder could be known a priori, — ^if, for in-
stance, it were possible to apply a manometer to
the cylinder, then would immediately be deduced
what is the friction of the engine corresponding to
that load.
In effect, since by h3rpothesis the pressure in the
cylinder or on the piston would be known, calcu-
lating the total effect of that pressure on the area of
the piston, we should have the exact valuation of
the power applied by the engine. Now, from other
sources is known also the resistance opposed to
the motion, for it consists of the gravity, the fric-
tion of the train, the resistance of the air, the
resistance caused by the blast-pipe, and the friction
of the engine.
Besides, if the engine, in drawing this load, were
constantly to increase its velocity, there would
plainly be excess of the power over the resistance ;
if, on the contrary, the velocity were gradually to
lessen, the power would be inferior to the resist-
ADDITIONAL FRICTION OF THB ENGINES. 225
ance ; but if the engine be observed at a moment
when it has acquired a certain uniform velocity, and
that velocity be maintained without alteration, the
effort then applied by the engine must necessarily
be precisely equal to the resistance which is op-
posed to it; for, were it not so, there would be
acceleration or retardation of motion.
Thus, the effort appUed by the engine and the
resistance opposed to the motion would be known,
and by making these two quantities equal to each
other, we should thence deduce the friction proper
to the engine.
This mode then would give immediately the fric-
tion of the engine, if the pressure in the cylinders
were known.
But there are cases wherein the pressure in the
cylinder is in effect known ct priori, and is no other
than the pressure in the boiler itself. These cases
are those wherein the engine attains the limit of its
power with the pressure at which it works, that is
to say, when it draws the greatest load it can draw
with that pressure.
In effect, since by hypothesis the engine has
attained the limit of its power, the pressure in the
cylinder cannot be less than in the boiler ; for if it
were, by diminishing the velocity, which is the only
obstacle to the equiUbrium of pressure being esta-
blished between the two vessels, we might give the
steam time to rise in the cyUnder to a pressure equal
to that of the boiler, and then the effect would be
Q
226 CHAPTER VIII.
augmented. That is to say, the engme would draw
a greater load, which is against the hypothesis. On
the contrary, as soon as the pressiire in the cylinder
is hecome equal to that of the boiler, no subsequent
diminution of velocity will admit of increasing the
load ; for that increase of load requires an increase
of intensity in the motive force, that is, in the
pressure of the steam on the piston, which is no
longer possible.
Thus, in the case wherein the maxunum load of
the engine is attained, we know it priori the effort
applied, and can, as has been explained above,
deduce from thence the corresponding friction of
the engine.
Suppose then, in an experiment, this limit of the
power of the engine to be attained. Let d be the
diameter of the piston, and w the ratio of the cir-
cumference to the diameter, lird^ will be the area
of one piston, and j^ird^ the area of the two pistons
together. Again, let (P— |>) be the effective pressure
of the steam, per unit of surface, during the experi-
ment ; it is clear, from what has been said above,
that ^ird^ (P— i^) will be the force which was then
applied on the piston.
Calling D the diameter of the wheel, and I the
length of the stroke, that force applied on the
piston was, on transmitting itself to the engine,
reduced in the inverse ratio of the respective veloci-
ties, or in the ratio — =r. Thus, after transmission
ttD
to the engine, it had for its expression :
ADDITIONAL FRICTION OF THE ENGINES. 227
This is then the expression of the force of traction
appUed to the progression of the engine.
Again, expressing by p'v the effective pressure
produced on the opposite face of the piston by the
action of the blast-pipe, the resistance thence re-
sulting against the progression of the engine was
, dH
Similarly, M being the weight of the load, and m
that of the engine, both expressed in tons, g the
gravity, in pounds, of a ton placed on the incUned
plane of the experiment, and, in fine, k expressing
the friction of the carriages per ton,
{k + g)M + gm
was the resistance opposed by the friction and the
gravity, in ascending the inclined plane. Finally, if
uv^ represent the resistance of the air, at the velo-
city of the motion, and X the unknown friction of
the loaded engine, we see that
{k + g)M + gm + uv^ +P^^ + X
was the total resistance opposed to the motion of the
engine.
As we have seen that, by reason of the uniformity
of the motion, the power was equal to the resistance,
it follows that we had
228 CHAPTER VIII.
(P-p) ^= (k + g)M + gm + uv^ + p'v^+X,
and consequently, in fine,
X = (P^p^p'v)^^{k + g) M-gm^uv'.
This equation therefore gives the friction of the
loaded engine.
To apply this expression to the numerical deter-
mination of the friction, attention must be paid to
the manner of expressing the different quantities
contained in it. P represents the total pressure of
the steam in the boiler, p the atmospheric pressure,
and p'v the effective pressure owing to the blast-
pipe ; and these forces act against the surface of the
piston. Thus, according as they are expressed in
pounds per square inch, or in pounds per square
foot, the diameter d of the piston must be measured
in inches of in feet. The length I of the stroke, and
the diameter D of the wheel, must be expressed
either both in feet or both in inches, which is
indifferent, since the equation contains only their
ratio. The quantities fc, g and uv^ must, as we have
said, be expressed in pounds, and in fine the defini-
tive value of X will equally be expressed in pounds.
Sect. II. Experiments on the additional friction of
locomotive engines.
The formula which we have just obtained is very
simple, and gives easily the friction of the engine
in all cases when it has attained the limit of its
ADDITIONAL FRICTION OF THE ENGINES. 229
power. All that remains to do, then, is to attain
that point. In consequence, we undertook a series of
experiments, sometimes taking the loads as great as
the engine could draw, at other times limiting our-
selves to a moderate load, but lowering the pressure
in the boiler by means of the safety-valve, as much
as possible without stopping the train.
The experiments in question were made on three
inclined planes of the Liverpool and Manchester
Railway, viz.: on the inclined plane of Sutton,
inclined ^, on that of Whistoriy inclined ^^ and
on the acclivity of ChatmosSy rising f^^o- ^ ^ti-
mating the resistance on these planes, we took
account of the gravity, as has been indicated in
Chapter VI. As to the resistance of the air and
that df the blast-pipe, we used the practical Tables
which we have given on the subject. For that
purpose, we note, in each experiment, the elements
proper for the use of the Tables, viz.: the velocity of
the engine, the mean vaporization of the boiler, the
area of the blast-pipe, and the nature of the train in
motion. With these data, there is no difficulty in
finding, without calculation, the quantities which
we have expressed above by uv'^ and pv ; and sub-
stituting them, with the dimensions of the engine
and the other data of the problem, in the formula
developed above, we thence conclude the additional
friction of the engine.
The results thus obtained in the different experi-
ments now before us, are collected in a Table which
230 CHAPTER VIII.
we shall presently offer : to show however the pro-
ceeding which we have followed, and to make the
nature of it better understood, we will here detail
the calculation of the first of those experiments.
On the 22d July, 1834, the engine Vulcan,
cylinder 11 inches, stroke of the piston 16 inches,
wheel 5 feet, weight 8*34 tons, effective pressure in
the boiler then 57*5 lbs. per square inch, ascended
the inclined plane of Sutton with a train of 6 first-
class coaches, the mail, and two empty trucks;
weight of the train, tender included, 39*07 tons.
The velocity of 26*6 miles per hour^ before reaching
the foot of the inclined plane, sunk to 7*5 miles per
hour at the top of the plane.
With these data, we have to calculate succes-
sively the effort appUed by the engine, and the
resistance which was opposed to it. Now, the
effective pressure observed in the boiler, was 57*5
fts. per square inch. Moreover, in this engine the
diameter of the blast-pipe was 2*25 inches, and the
mean vaporization 60 cubic feet of water per hour.
Consequently, from the Table given above, the re-
sistance against the piston, caused by the blast-pipe,
at the velocity of 7' 5 miles per hour, was 1*3 ft.
per square inch. The real disposable force of the
engine then was 57*5 — 1*3= 56*2 fts. This is
the quantity which we have represented above by
(P—p—pv),
This premised, the effort exerted by the engine
might be calculated thus :
ADDITIONAL FRICTION OF THE ENGINES. 231
1 90 . . . Area of the two pistons, in
square inches^multiplied by
56'2fts. Real effective pressure of
the steam per square inch
on the piston, gives
10678 lbs. Force appUed on the pis-
ton; which, transmitted as
force of traction to the en-
gine, whose velocity is 59
times as great, gives
= 1810 lbs. Definitive effort applied by
the engine.
On the other hand, the resistance was :
3907x6=234 lbs. Resistance owing to the
friction of the carriages.
^Q =1193 lbs. Resistance caused by the
gravity of the total mass,
train and engine, on the
plane inclined ig ;
25fts. Resistance of the air against
an effective surface of 1 70
square feet, at the velocity
of 7*5 miles per hour.
1452 lbs. Total resistanceof the train.
Consequently, subtracting first the resistance of
the train from the effort exerted by the engine, we
have
232 CHAPTER VIII.
1810
-1452
358 lbs.,
which is the total friction of the engine, corre-
sponding to the above load. Moreover, if we again
subtract 125 lbs. for the friction of the unloaded
engine, there remains
358
-125
233 lbs.;
and this number consequently indicates the addi-
tional friction created in the engine by the resistance
of 1452 lbs. Finally, then, the additional friction
created by each pound of resistance or of traction
imposed on the engine, is
233
1452
= 161 ft.
The other calculations are performed in a manner
entirely similar. For this reason we content our-
selves with presenting the data and the results of
them in the following Table.
We have made a distinction between the engines
with uncoupled wheels, and those with coupled
wheels, because it is evident that in the latter,
whose wheels are held together by connecting rods,
the motion is communicated by a greater number of
joints, and consequently all that tends to produce
an additional friction must produce a more con-
siderable one in them than in the engines with
unconnected wheels.
ADDITIONAL FRICTION OF THE ENGINES. 233
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234 CHAPTER VIII.
From these experiments, we perceive that in
engines with uncoupled wheels, the additional
friction created per ft. of traction is '137ft., that
is to say, the friction is about j- of the resistance
imposed on the engine; and that in engines with
coupled wheels it amounts to '215ft., or may be
taken at half as much more than the precedmg.
It will readily be conceived, however, that it must
vary with the construction and state of every en-
gine. This is observable particularly in the engine
Vesta, which, at the moment of the experiments,
was not in a state of repair altogether satisfactory.
With reference to the manner in which the addi-
tional friction of engines ought to be calculated, we
have to recall to mind that it is to be reckoned on
every pound of the total resistance exerted against
the motion ; that is to say, the resistance caused by
the friction of the waggons, that of gravity, and that
of the atmospheric air, must first be calculated, and
on the sum of these the additional friction of the
engine is to be taken at the rate already indicated.
It was in fact only by first introducing these dif-
ferent resistances into the account, that we have
attained the above result; and consequently there
can be no misunderstanding as to the manner in
which the calculation should be done.
With respect to the resistance created directly on
the piston, either by the atmospheric pressure or by
the pressure arising from the blast-pipe, as these
forces are destroyed by the opposed pressure of the
ADDITIONAL FRICTION OF THE BNGINES. 235
steam immediately, without the interposition of any
action on the part of the mechanical organs of the
engine, it is evident that they can create no addi-
tional friction in the engine. They ought not there-
fore to enter into this account.
Sect. III. New developements on the mode of deter-
mination employed.
An increase of friction in proportion to the load
is foimded on principle, as we have proved, and the
mode of calculation which we have used will give
exactly the measure of it, provided the engine be
really arrived at the limit of its power with a given
pressure, that is to say, at the m,aximum load that it
can draw at that pressure. For the cases in which
the engine slackened its velocity to the rate of 2 or
3 miles per hour, that point was evidently attained,
since the engine was literally on the point of stop-
ping. But moreover, it will presently be seen that
for all cases in which the uniform velocity did not
exceed 10 or 12 miles per hour, we were equally
justified in taking the pressure on the piston as
equal to that in the boiler.
In effect, the steam being at a certain degree of
pressure in the boiler, passes into the steam-pipe,
and from thence into the cylinder, where it at first
expands, and would promptly rise to the same de-
gree of pressure as in the boiler, if the piston were
immoveable. This piston, however, offering on the
236 CHAPTER VIII.
contrary but a certain resistance determined by the
load which the engine draws, 40fts. per square
inch for instance, will recede as soon as the elastic
force of the steam in the cylinder shall have at-
tained that point. A piston which withstands a
resistance of but 40 lbs. per square inch, is nothing
more than a valve loaded with 40 lbs. per square
inch. If the communication between the boiler and
the cylinder were completely open and without tube
or contraction, the piston would become in reality a
valve to the boiler ; and that valve yielding before
the safety-valve which is loaded, for instance, with
50fts. per square inch, the steam in the boiler
could not rise above 40 lbs. As, however, the
passage is contracted, the piston is not a valve
to the boiler; but it still remains one for the
cylinder.
From these three points it results : 1st, that the
pressure in the cylinder is strictly equal to the re-
sistance on the piston ; 2ndly, that it is because the
piston gives way and recedes before the steam, that
the latter qannot augment its pressure beyond that
point, and rise to the pressure of the boiler ; but if
by any means whatever the piston were rendered
immoveable, or only that it did not give way faster
than the steam is generated at the pressure of the
boiler, an equilibrium of pressure would at once be
established between the cylinder and the boiler ; and
3rdly, that if there be in the steam-pipe a velocity
greater than that which corresponds to the velocity
ADDITIONAL FRICTION OF THB ENGINES. 237
of generation of steam in the boiler, it is because the
pressure is less in the cylinder than in the boiler, and
that the fluid consequently seeks to settle in equili-
brio in the two vessels. These observations show that
the eflfective pressure on the piston may be calcu-
lated by that which exists m the boiler, as soon as
the velocity of the piston is reduced to that of the
generation of the steam. As we shall soon know by
experiment, what is the total mass of steam, at the
pressure of the boiler, produced by the engine in a
given time, it will be easy to calculate how many
cylinders full of steam, at that same pressure, the
engine can supply in a minute, and thus what is
the velocity which corresponds to what we call fall
pressure in the cylinder. We shall then see that for
the engines under consideration, it is from 10 to 12
miles per hour, or thereabout. We may then con-
sider that, in all the cases of uniform motion,
wherein the velocity did not exceed that rate, the
pressure in the cylinder was the same as that in the
boiler; and therefore, in so calculating it, we had
the exact measure of the power then applied by the
engine.
CHAPTER IX.
OF THE TOTAL RESISTANCE ON THE PISTON. RE-
SULTING FROM THE DIVERS PARTIAL RESIST-
ANCES PRECEDENTLY MEASURED.
Wb have just estimated successively, in the pre-
ceding chapters, the divers resistances which oppose
the motion of the engine. It is necessary now to
seek the definitive resistance which results from
them united, per square inch or per unit of surface
of the area of the piston.
The resistances which we have hitherto con-
sidered are : the resistance of the air, the friction
of the waggons, the gravity, the friction of the
engines, and the resistance arising from the hlast-
pipe. But we must here add, besides, the atmo-
spheric pressure ; for the engines under consideration
being high-pressure engines, it follows that the op-
posite face of the piston necessarily supports, like
every other body in conununication with the atmo-
sphere, a certain pressure due to the elasticity of
the atmospheric air.
In the calculations which we have hitherto made,
we were enabled to suppress that force in the re-
sistance, because at the same time we equally sup-
OF THE TOTAL RESISTANCE ON THE PISTON. 239
pressed it in the power, by calculating the latter
only according to the effective pressure of the steam,
that is to say, according to its siurplus over the
atmospheric pressure. This mode of proceeding
was correct then, because, having to consider the
power and the resistance only in the case of equality
or equilibrium, and unmixed with any other con-
sideration, we could without error retrench on both
sides the same quantity. But as, in other questions
which are about to present themselves, we shall
want to consider the steam with reference to its
volume, and as that volume depends on the total
pressure at which the steam is generated, we must
retain that total pressure, to express the elastic
force of the steam ; and consequently, must also let
the atmospheric pressure remain in the resistance
opposed to the motion of the piston.
Thus, the definitive resistance exerted against the
piston consists of six resistances, which are : the
friction of the waggons, the resistance of the air,
the gravity of the train, the friction of the engine^
the atmospheric pressure, and the pressure caused
by the blast-pipe. Of these six resistances, the last
two act immediately and directly on the piston.
They must therefore be moved at the velocity of
the piston itself; but it is not so with the other
four. It has already been said that in an engine,
the pressures exerted on different points by the
same force, are in the inverse ratio of the velocities
of those points. Here the engine and its train must
240 CHAPTER IX.
be moved at a velocity greater than that of the
piston, in the proportion of the circumference of
the wheel, to twice the length of the stroke. The
intensity of the pressure exerted by the resistance
of the load, the air, the engine, and the gravity, is
then increased by its transmission to the piston, in
the above ratio of the velocity of the wheel to that
of the piston.
Consequently, if M express the number of tons
gross which compose the total load, that is to say,
including the weight of the tender-carriage of the
engine, and k the number of pounds requisite to
draw one ton on a railway,
kU
will be the resistance, in pounds, resulting from the
friction of the waggons which carry the load. If at
the same time we call g the gravity of 1 ton on the
inclined plane to be traversed by the engine, and if
m represent the weight of the engine, in tons,
g {M + m)
will be the resistance, in pounds, produced by the
gravity of the total mass, train and engine ; so that,
according as the motion takes place in ascending or
in descending, the definitive resistance arising from
friction and gravity will be
kM±g (ML + m) = {k±g)M± gm.
Similarly, if we express by uv^ the resistance, in
pounds, exerted by the air against the train, at
the velocity v of the engine.
OF THE TOTAL RESISTANCE ON THE PISTON. 241
{k ± g) M ± gm-^- uv^
will be the resistance opposed to the motion of the
.engine by the friction, the gravity, and the shock of
the air.
If, again, F represent the friction of the unloaded
engine, expressed also in pounds, and S its additional
friction, measured as a fraction of the resistance, as
has been indicated in Chap. VIII., we see that
F + S[(k±g)M±gm + uv^]
will be the total friction of the engine at the moment
when it draws the resistance
(fc ± jr) M ± jfm + wv^«
Consequently
(1 + S) [(ft ±g)M±gm + uv^] + F
will be the total resistance opposed to the progres-
sion, along the rails, by the engine and its train.
As this force produces on the piston a resistance
augmented in the ratio of the circumference of the
wheel to twice the stroke of the piston, if D express
the diameter of the wheel, I the length of the stroke,
and w the ratio of the circumference to the diameter,
vD ttDF
(1 +8) [(fcljr) M ±srm + Mt;T -2|- + -gT
will be the resistance on the piston, caused by that
force, that is to say, caused by the resistance of the
waggons, the gravity, the air, and the friction of the
engine.
R
242 CHAPTER IX.
This resistance is that which is exerted on the
totality of the area of the pistons. But representing
by d the diameter of the cylinders, ^ird^ will be the
area of the two pistons. Whence
ttD . •jtDF
(1 + S) [(& ±g)M±gm + uv^] -^ + -^
or, simplifying,
D . DF
(1 + S) [(fc ±g)M±gm + wt;^ ^ + -^j>
will be the same force, divided according to the unit
of surface of the piston.
Adding to this the atmospheric pressure ji, and
the pressure caused by the blast-pipe j> v, which are
already measured per unit of surface, we shall have
in fine, for the total resistance R exerted on the
piston,
D DF
R=(l+S)[(fc±(/)M±(7m+iit;^] -^^i+^+P+pv.
In this expression, the quantity g represents the
gravity on the plane to be traversed by the train ; if
the plane be horizontal instead of inclined, we shall
have 5^=0. The weights M and m of the train and
the engine are expressed in tons gross ; the quantity
k^ which is the friction of the waggons per ton, is
equal to 6ibs. ; the value of S is '137 or -f* for
engines with uncoupled wheels; the velocity t; of
the engine is expressed in miles per hour ; in fine,
according as the dimensions D, / and d are expressed
OF THE TOTAL RESISTANCE ON THE PISTON. 243
in inches or in feet, and the forces w, p and p\ in
pounds per square inch, or in pounds per square
foot, the value R which will result from the calcu-
lation will be the resisting pressure on the piston,
expressed likewise in pounds per square inch, or in
pounds per square foot.
Applying this calculation to a train of 9 waggons
and a tender, weighing 50 tons gross, and drawn at
the velocity of 20 miles per hour, up a plane in-
clined 3^, by an engine with two cylinders of 1 1
inches diameter, stroke of the piston 1 6 inches, pro-
pelling wheels 5 feet, not coupled, weight 8 tons,
friction 104 ibs., blast-pipe 2*25 inches in diameter;
and referring, for the resistance of the air, to what
has been said in Chapters IV. and VI., the proceed-
ing will be as follows :
50 X 6=300 fcs. Friction of the waggons, in
pounds, or value of fcM.
2240
-Tjjw>X 58=260 ibs. Gravity of the total mass,
train and engine, or value of
g (M+m).
194fts. Resistance of the air against
an effective surface of 180
square feet, at the velocity
of 20 miles per hour, or
value of let?*.
754 fts. Resistance of the train, or
(fc + S') M+jfm + Mi;^
244 CHAPTER IX.
754Xl'137=857Ste. Resistance of the train, in-
cluding the additional fric-
tion which it produces in the
engine, or
+ 104 lbs. Friction of the unloaded en-
gine, or F.
961 fts. Total resistance to the pro-
gressive motion of the en-
gine, or value of the term
(1+S) H]c+g)M+gm+uv'^+F.
On the other hand, we have
3- 1416 X 60 in.= 1885 Circumference of the wheel,
expressed in inches, or wD.
2xl6in.= 32 Double the stroke of the
piston, expressed in inches,
or 21.
188-5
32
5*9 Ratio of the velocities of
the wheel and the piston,
or
21
Thus,
961 X 5*9=5670 fts. Resistance produced on the
piston, or value of the term
OF THB TOTAL RBSISTANCB ON THE PISTON. 245
Again,
31416X11^ inn A 4- .1. f
g = 190 Area of the two pistons, in
square inches, or ^wd^.
Consequently, we obtain in fine
-ToQ =29'8fcs. Above-mentioned resistance,
portioned per square inch
of the surface of the piston.
-f 3'5fi>s. Effective pressure per square
inch, arising from the blast-
pipe, or p'v.
-{-14' 7 lbs. Atmospheric pressure per
square inch, or p.
48 '0 lbs. Definitive resistance, per
square inch of the surface
of the piston of an engine
with two cylinders of 11
inches in diameter, &c.,
when drawing a load of 50
tons under the given cir-
cumstances.
Were it desired to know that resistance per square
foot, it would suffice to multiply the last result by
144, that is to say, the pressure required would be
6912 S>s. per square foot, which number would have
been obtained directly, if instead of expressing the
area of the piston in square inches, and the partial
246 CHAPTER IX.
pressures ia pounds per square inch, these measures
had been referred to the square foot as unit of
surface.
This example shows what is to be understood by
the different quantities contained in the formula,
and how each of them ought to be introduced into
the calculation.
CHAPTER X.
OF THE VAPORIZATION OF LOCOMOTIVE ENGINES.
Sect. I. Experiments on the vaporization of loco^
motive engines.
So far our object has been to estimate the re-
sistance offered to the motion of locomotives, ac-
cording to the circumstances of their load and of
their velocity. It will now be proper to value the
power of which they can dispose to overcome that
resistance ; and as we have already made known
the means of measuring one of the elements of that
power, viz., the elasticity or pressure of the steam
in the boiler, it remains only to seek what quantity
of that steam can be produced by the engine in
different circumstances, and in a given time.
For this purpose we undertook a series of expe-
riments on the vaporization of locomotives, taking
the engines successively either working without the
aid of the blast-pipe, or with divers orifices of blast-
pipe and different velocities, or, in fine, under
different pressures in the boiler. We shall first
give an account of these experiments, and then
examine the influence of each of the circumstances
248 CHAPTER X.
just mentioned, on the vaporization produced by
the engine.
Among the experiments of which we are now
going to present the results, the first three were
made on engines at rest, and without the appli-
cation of the blast-pipe, that is to say, without
employing the waste steam in exciting the fire.
The vaporization produced was therefore due simply
to the natural draught of the chimney. In all the
other experiments use was made of a blast-pipe,
large or small, as will be seen indicated in the
Table which we shall present further on.
To know the quantity of water vaporized by the
boiler, the proceeding was this. As all the tender-
carriages of the Liverpool and Manchester Railway,
on which the experiments were made, have exactly
the same dimensions, it was ascertained first of all,
by weighing one of them when empty and when
full, that every inch of depth of the water in the
tank corresponded exactly to a weight of 206'5fts.,
or 3*304 cubic feet of water. This established, the
next thing done was to ascertain, by means of the
glass-tube, the depth of the water in the boiler at the
beginning of the experiment, and at the same time
the exact depth was taken of the water contained
in the tank ; afterwards, when the experiment was
concluded, the boiler was first filled up to the height
at which it was originally, and then the water re-
maining in the tank was measured. The difierence
between the two depths of water in the tank, gave
OF THE VAPORIZATION OF THE ENGINES. 249
the consumption that had been made of it during
the time of the observation.
As the experiments made with engines at rest,
that is to say, without the application of the blast-
pipe, show that in this state the engines are capable
of effecting about ^ of their vaporization with the
aid of the blast-pipe, use has been made of this
datum to take account, in the different experiments,
of the vaporization which had taken place during
the stoppages of the engine, and during the descent
of the inclined planes, on which the engines run of
themselves, without making use of the steam. It is
evident, in fact, that during this time, as well as
during the delays which took place on the road, the
fire was no longer excited by the action of the blast-
pipe, and the vaporization was necessarily reduced
in consequence. As the experiments took place on
the Liverpool and Manchester Railway, which has, in
each direction, a declivity of the kind we have just
mentioned, and the descent of which, with the use
of the brake, is performed in 5 minutes, we have,
in all the cases, taken 5 minutes for the duration of
the suspension of the action of the blast-pipe re-
lative to that circumstance. Thus, for instance, in
experiment VI., the engine Star stopped 15 minutes
on the road. Besides this, the descent of the in-
cUned plane occupied 5 minutes. Out of the total
duration of the experiment, there were then 20
minutes during which the action of the blast-pipe
was suspended. As, during this time, the engine
250 CHAPTER X.
vaporized the same quantity of water that it would
have done in 4 minutes, had it worked with the aid
of the blast-pipe, it is plain that these 20 minutes
of delay may be replaced by 4 minutes of forced
vaporization. Thus the experiment is the same as
if the 130*90 cubic feet of water consumed by the
engine, had been vaporized in 1 hour 56 minutes of
uninterrupted work; which gives 67*71 cubic feet
for the vaporization effected per hour, during the
appUcation of the draught of the blast-pipe. In
this manner the numbers contained in the last
column but one of the Table, were deduced from
the observations. It is to be remarked, that the
delays which took place during these experiments
were caused by various essays made on the engines.
To obtain the mean velocity of the motion, we
divided the total distance performed, which was
29*5 miles, by the total time of the experiment,
minus the delajrs which took. place on the road;
but in some experiments the engines ascended the
inclined plane twice, which increased the total dis-
tance performed to 32*5 miles instead of 29*5 ; and
in those cases we have taken account of that cir-
cumstance.
In all the experiments we give the pressure m
the boiler from direct observation. In experiments
I. and II. the boiler was not placed on the engine,
and was open to the air, that is to say, the steam-
dome and the cover of the man-hole were taken
off; so that the vaporization went on under the
OF THE VAPORIZATION OF THE ENGINES. 251
atmospheric presBure, or under an effective pressure
null.
' Before beginning any experiment^ we waited till
the steam made the valves blow, which showed that
the vaporization was in full activity; and in the
experiments L and II., in which there was no valve,
before beginning to note the quantity of water va-
porized, we left the fire alight under the boiler for
several hours, in order to be assured that the water
effisctually boiled in all its parts ; and the non-ful-
filment of .this condition made us reject several
experiments.
In fine, we give approximately the state of the
temperature of the water in the tend^, at the mo-
ment the engine started, because there must in-
dubitably result firom it an increase in the definitive
vaporization of the engine ; but as that temperature
was not noted with sufficient accuracy, as it di-
minishes, moreover, during the experiment, and
lastly, as it may easily be compensated by a superior
quality in the fud, or by more care on the part of
the engine-man in stoking the fire, we are satisfied
merely to point out its natural influence on the
results, without seeking to take account of it with
precision.
In the following Table, which presents the results
of these experiments, we group together those en-
gines in which there is sensibly a like proportion
between the heating surface of the fire-box and that
of the tubes. The object of this distinction will be
252 CHAPTER X.
to seek, firstly, whether there results from it any
difierence in the vaporizing power of the engines in
a given time; and again, whether there results'
therefirom any saving in the consumption of fuel in
producing that vaporization. This second research
will be the subject of the following chapter.
It will be remarked that the Table contains two
difierent engines of the name of Firefly. The
reason is, as we have said elsewhere, that on re-
constructing that engine, the dimensions of the
boiler had been changed, and it wbs proper there-
fore to distinguish the two engines by a different
number. In like manner, the boiler under the
name of Goliath II. was a new boiler, constructed
to replace that which the engine had originally, and
whose dimensions are given in the Table, page 37
of this work. The new boiler, however, of the
Goliath, instead of being placed on the engine for
which it had been made, WBS used as a stationary
boiler at the Edge-Hill station, on the Liverpool and
Manchester Railway. It was there that we submitted
it to experiment, with the aid of Mr. Edward
Woods, now the Company's engineer, who is well
known to evince as much skill as care in whatever
researches he undertakes.
OF THE VAPORIZATION OF THE ENGINES. 253
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254 CHAPTER X.
Sbct. II. Of the influence of the pressure in the
boiler on the vaporization of the engine.
In treating (Chapter II. of this work) of the laws
which regulate the mechanical action of the steam,
we have shown that the steam in contact with the
liquid, under all degrees of tension, contains always
the same total quantity of heat. Hence it follows,
evidently, that to vaporize a given weight of water,
under any pressure whatever, the same quantity of
heat must always be communicated to it, that is to
say, the same quantity of fiiel must be consumed in
the same boiler ; and consequently too, a given
consumption of fuel will always correspond to the
vaporization of the same weight of water in the
same boiler, whatever be the pressure under which
that vaporization is effected.
To comprehend clearly how it is that the steam
can be generated at a higher or lower degree of
pressure by the same application of heat, we must
consider what passes in the boiler during the ebul-
lition of the water. Suppose a boiler filled with
water to a certain level, and containing, above that
level up to the dome of the boiler, a vacant space of
1728 cubic inches, capable of being filled with
steam. Suppose, moreover, that the boiler be
placed above a furnace filled with Ughted coal,
emitting a certain quantity of heat per minute. As
soon as the fire shall have transformed into steam
1 cubic inch of the water contained in the boiler,
OF THE VAPORIZATION OF THE ENGINES. 255
the steam thus generated will fill the vacant space
just mentioned; and since we have supposed the
capacity of that space to be 1 728 cubic inches, that
is to say, 1728 times the volume of the water va-
porized, it follows that the steam which occupies that
space will have a relative volume equal to 1728
times the volume of the water. Now, recurring to
the Table which we have given (Chapter II. of this
work), and which is deduced irom experiment, it
will be recognised that, when the relative volume of
the steam is expressed by the number 1728, the
total pressure of that steam is then about 15 lbs.
per square inch, and its sensible temperature about
212 degrees of Fahrenheit. Thus, at this moment,
the steam contained in the boiler will be at the
pressure of 15fbs. per square inch. Supposing
then the safety-valve to be loaded only with the
atmospheric pressure, which is also very nearly
159>s. per square inch, we perceive that, if the
safety-valve is large enough, the pressure in the
boiler will never rise above that point, because the
steam will escape by degrees as it is produced ; and
consequently, whatever be the intensity of the fire,
that is to say, in whatever quantity the steam be
generated, it will still continue to be in the boiler at
the pressure of 15fbs. per square inch, and at the
corresponding temperature, or 212 degrees of Fah-
renheit.
But if we suppose the safety-valve of the boiler
to be loaded with 50 9>s. per square inch, over and
256 CHAFTBR X.
above the atmospheric pressure, this is what will
take place. At the moment when there is but one
cubic inch of water vaporized, it will fill, as we have
said, the vacant space in the boiler, and will be, as
before, at the pressure of 15 lbs. per square inch,
and at the sensible temperature of 212 d^;rees.
But, as the fire continues its action, the steam
being no longer able to escape by degrees as it is
produced, on account of the resistance of the valve,
the vaporized water will accumulate in the boiler,
that is, in the same vacant space of which we have
given the capacity. When, therefore, 2 cubic inches
of water shall be vaporized, since these 2 cubic
inches will still occupy a space of 1728 cubic
inches, it is plain that the volume of the steam
compared to that of the water which produced it,
that is, the relative volume of the steam, will be
expressed by the number 864. Hence, from the
same Table above mentioned, the steam resulting
fit>m the vaporization of these two cubic inches of
water will be in the boiler at the total pressure of
31 lbs. per square inch, and at the saasible tem-
perature of 253 degrees, which corresponds to that
pressure. As, however, the pressure of 31 lbs. will
not suffice to raise the valve and admit of the steam
escaping by degrees as it is generated, the steam
produced by the action of the fire will continue to
accumulate in the boiler. When 3 cubic indies of
water shall have been vaporized, the pressure in the
boiler will be 48 Jb&. per square inch, and the t^n-
OF THE VAPORIZATION OF THE ENGINES. 257
perature 280 degrees ; and, in fine, when there
shall be 4 cubic inches of water transformed into
steam, the pressure will have risen to 65 lbs. per
square inch, and the temperature to 299 degrees of
Fahrenheit. But at this moment the pressure of
the steam will have become equal to the weight of
the valve, and, in consequence, the latter will be
raised. Whence, reckoning from this moment, and
provided the safety-valve be large enough, the pres-
sure and the temperature of the steam will continue
to maintain themselves at the same degree, what-
ever may be the vaporization produced. But now,
if we suppose that the fire retains in all cases a
constant intensity, capable of communicating per
minute to 1 cubic inch of water a quantity of heat
expressed by 1170 degrees of Fahrenheit, or 650
degrees centigrade, we see that the boiler will be
enabled to change 1 cubic inch of water into steam
every minute, and that the cubic inch, thus trans-
formed, will assume, according to the weight of the
valve, 159>s., or 31 fts., or 48 lbs., or, in fine,
65 fi>s. per square inch. And each of these effects
will be produced without it being necessary to sup-
pose that the fire has acquired any more intensity,
that is to say, without any more fuel being con-
sumed in one case than in the other.
Thus it is seen that the vaporization resulting
from a given consumption of fuel must always be
sensibly the same, under whatever degree the steam
in the boiler be generated. This, in fact, is con-
s
258 CHAPTER X.
firmed by the experiments we have just presented.
A slight advantage even is perceptible in those
engines which work at higher pressure ; for the
Goliath II. , working under the atmospheric pres-
sure, vaporized on an average '036 cubic foot of
water per hour and per square foot of heating sur-
face ; and the Firefly II., under the effective pres-
sure of 50 lbs. per square inch, instead of producing
less, vaporized per hour and per square foot of
heating surface, a quantity of water which amounted
to '037 cubic foot. The other examples offer similar
results. For instance, in the two experiments V.
and VI., the Star, with the same blast-pipe and
very nearly the same velocity, vaporized a greater
quantity of water per hour under the pressure of
45 lbs. per square inch, than under that of 38*7;
and we find the same result in the experiments
XXI. and XXQ. made with the engine Atlas.
Considering the vaporization independently of
the consumption of fuel, that is to say, seeking
merely the quantity of water which the engines can
vaporize per hour, without regard to the corre-
sponding expenditure of fuel, we ought not to be
surprised to find in general that the engines which
work at a higher pressure produce a greater vapor-
ization per hour. The reason is, that when the
safety-valve of an engine is fixed, for instance, at
50 lbs. of eflfective pressure per square inch, it is
less liable to blow, that is, to let the steam escape,
than when it is fixed only at 40 lbs. of eflfective
OF THE VAPORIZATION OF THE ENGINES. 259
pressure per square inch. In the latter case, then,
the engine-man will see the valve blow more fre-
quently, and this being for him a sign that his fire
is as lively as need be, he will not serve the fire-box
with the same activity; the result will be that he
will indeed consume less fiiel, but he will produce
less vaporization per hour in the engine.
Thus, to recapitulate, we see that the vaporiza-
tion in the engines is independent of the pressure
in the boiler, and that even, when the vaporization
is considered without regard to the corresponding
expenditure of fuel, it is in general found more
considerable under a high pressure than under a
low one.
Sect. III. Of the influence of the velocity of the
engine on the vaporization of the boiler.
It has been seen (Chapter VII.) that the pressure
in the blast-pipe varies in the direct ratio of the
velocity of the motion, and in the inverse ratio of
the area of the blast-pipe. On the other hand, it is
known that the draught which takes place in the
fire-box is the result of the velocity assumed by the
steam in the blast-pipe, and, consequently, in the
chimney by reason of that pressure. It is natural
then to think that the velocity of the engine and
the size of the orifice of the blast-pipe must have an
influence more or less considerable on the vapor-
ization produced in the boiler.
260
CHAPTER X.
In effect, on perusing the experiments which we
have just presented, the influence of the velocity on
the vaporization plainly appears ; for, collecting the
experiments made on the same engine and with the
same blast-pipe, but with a different velocity, we
form the following Table.
Experiments on the influence of the vehcUy of the engines
on the vaporization of their boiler.
Number
of the
expoiment.
Name of
the engine.
Aram of the
blast-pipe.
Velocitj,
in milea per
hour.
Vaporisation
p«r hour.
State of Uie water
in the tender.
{Ji.
Star.
sq. in.
3-13
miles.
14-45
1513
cubic feet.
68-79
67-71
Very hot
Almost cold.
lix.
Star.
6-25
17-35
18-32
60-64
61-05
Hot.
Lukewann.
r xiii.
txiv.
FiesfltI.
3-98
17-70
21-33
6410
77-31
Almost cold.
Lukewarm.
rxv.
1 XVI.
FURT.
3-65
18-63
19-67
57-46
54-45
Cold.
Cold.
rxvii.
t XVIIL
Lbbos.
3-65
18-63
21-99
63-18
68-82
Scarcely tepid.
Very hot.
rxx.
^XXI.
[xxii.
Atlas.
6-78
7-37
6-78
8-99
15-00
15-53
43-81
5000
48-21
Cold.
Cold.
Cold.
1
Comparing together those of the above experi-
ments which were made with the same orifice of
blast-pipe, and which we have, for that reason,
united with a bracket, it appears that with the
exception of the experiments V. and VI., XV. and
XVI., in which, however, the change of velocity
was quite inconsiderable, increase of velocity was
OF THE VAPORIZATION OF THE ENGINES. 261
invariably attended with increase of vaporization;
but the extent of that increase seems to have been
modified by the temperature of the water in the
tender. Thus in the experiments XIII . and XIV.,
as well as in the experiments XVII. and XVIIL,
the circumstance of the heat of the water in the
tender has co-operated with that of the velocity
to increase the vaporization, in the same manner
as in the experiments V. and VI. that circumstance
seems to have more than counterbalanced the then
contrary effect of the velocity. It is only therefore
by comparing together the experiments made with
the engine Atlas, that we can form a tolerably
exact notion of the influence of the velocity on the
vaporization. In effect, in the three experiments
made with that engine, the heat of the water in the
tender was the same ; the blast-pipe had not per-
ceptibly varied, and, with respect to the velocity,
there was difference enough to give room to hope
that other accessory circumstances would not be of
weight sufficient to counterbalance its effect. The
first of these experiments might then be compared
to a mean taken between the two others ; but as in
the third, the safety-valve of the engine was de-
signedly fixed at a very low pressure, viz., 30fts.
per square inch instead of 50, and as that circum-
stance, by making the valve blow too easily, occa-
sioned the engine-man not to keep up his fire with
the same intensity as in the other experiments, we
262 CHAPTER X.
shall have a more exact result hy comparing only
the experiments XX. and XXI.
Now, in the first, the engine, at the velocity of
8'99 miles per hour, vaporized 43'81 cubic feet of
water, or * 1 72 cubic foot per square foot of heating
surface ; and in the second, the same engine, at the
velocity of 15 miles per hour, vaporized SO'OO cubic
feet of water, or ' 1 97 cubic foot per square foot of
heating surface. These numbers are almost in the
precise ratio of the fourth roots of the velocities*
We may therefore conclude that the vaporization,
in locomotive engines, varies very nearly in the
ratio of the fourth root of the velocity of their
motion.
This variation is, as we see, of slight importance
in the most ordinary cases; but when very great
difierences of velocity are concerned, like those, for
instance, which take place in ascending inclined
planes, where the velocity is often reduced to the
half or the third of what it is on an average during
the rest of the trip, we perceive that it then acquires
a considerable influence, and consequently must not
be omitted in the calculation. We shall take ac-
count of this efiect in all the examples to be treated
of in the sequel ; but it is easy to see, at the same
time, that in a great number of practical applica-
tions it may be dispensed with.
OF THE VAPORIZATION OF THE ENGINES. 263
Sect. IV. Of the influence of the orifice of the blasts
pipe on the vaporization of locomotive engines.
If attention be now directed to the effects of the
blast-pipe, with reference to the vaporization, and
if, with this view, the first series of the experiments
already presented, in which no blast-pipe was used,
be compared to the other series, in which, on the
contrary, use was made of a blast-pipe more or less
reduced in size, it will at once be observed that the
application of the waste steam to the urging of the
fire produces a very important effect, and that it
nearly quintuples the natural vaporization of the
boiler. But seeking afterwards what modification
that effect undergoes from the narrowing more or
less of the blast-pipe, we do not observe a very
marked result in that respect.
Examining, for instance, the experiments made
with the Star, in which the alterations in the orifice
of the blast-pipe enable us to study its influence on
the vaporization of the boiler, and referring, accord-
ing to what has been said in the preceding section,
the effects produced to the velocity of 20 miles per
hour, we form the following Table.
262 CHAPTER X.
shall have a more exact result by comparing only
the experiments XX. and XXI.
Now, in the first, the engine, at the velocity of
8*99 miles per hour, vaporized 43'81 cubic feet of
water, or * 1 72 cubic foot per square foot of heating
surface ; and in the second, the same engine, at the
velocity of 15 miles per hour, vaporized 50*00 cubic
feet of water, or ' 1 97 cubic foot per square foot of
heating surface. These numbers are almost in the
precise ratio of the fourth roots of the velocities*
We may therefore conclude that the vaporization,
in locomotive engines, varies very nearly in the
ratio of the fourth root of the velocity of their
motion.
This variation is, as we see, of slight importance
in the most ordinary cases; but when very great
differences of velocity are concerned, like those, for
instance, which take place in ascending inclined
planes, where the velocity is often reduced to the
half or the third of what it is on an average during
the rest of the trip, we perceive that it then acquires
a considerable influence, and consequently must not
be omitted in the calculation. We shall take ac«
count of this effect in all the examples to be treated
of in the sequel ; but it is easy to see, at the same
time, that in a great number of practical applica-
tions it may be dispensed with.
OF THE VAPORIZATION OF THE ENGINES. 263
Sect. IV. Of the influence of the orifice of the blasts
pipe on the vaporization of locomotive engines.
If attention be now directed to the effects of the
blast-pipe, with reference to the vaporization, and
if, with this view, the first series of the experiments
already presented, in which no blast-pipe was used,
be compared to the other series, in which, on the
contrary, use was made of a blast-pipe more or less
reduced in size, it will at once be observed that the
application of the waste steam to the urging of the
fire produces a very important effect, and that it
nearly quintuples the natural vaporization of the
boiler. But seeking afterwards what modification
that effect undergoes from the narrowing more or
less of the blast-pipe, we do not observe a very
marked result in that respect.
Examining, for instance, the experiments made
with the Star, in which the alterations in the orifice
of the blast-pipe enable us to study its influence on
the vaporization of the boiler, and referring, accord-
ing to what has been said in the preceding section,
the effects produced to the velocity of 20 miles per
hour, we form the following Table.
264
CHAPTER X.
Experiments on the influence of the diameter of the blast-
pipe on the vaporization of boilers.
Number
of the
experiment.
Area of the
blast-pipe.
Vaporization per sq. foot
of total heating surface,
at the velocity of 20 miles
per hour.
VIII.
X.
V.
VI.
IV.
XI.
VII.
IX.
sq. inches.
1-25
2-50
313
313
3-75
4-38
6-25
6-25
cub. foot per hour.
•227]
;?^; Uo6
•197J
•190/ ^^"
From these results, it appears that for this engine,
of which the vaporization and heating surface have
been given above, a blast-pipe of 3 to 4 square
inches of area, or 2 to 2| inches in diameter, pro-
duces an average vaporization of about '206 cubic
foot of water per square inch of heating surface, per
hour ; that the contracting of the blast-pipe within
1*25 and 2*50 square inches, in nowise augments
the vaporization, but even tends rather to diminish
it ; and in fine, that the enlarging of the blast-pipe
to 6*25 square inches, produces a slight diminution
of from '206 to ' 1 90 cubic foot of water per square
foot of heating* surface.
These effects will easily be explained, from the
considerations which we shall offer in the next
section, on the comparative vaporization of the
OF THE VAPORIZATION OF THE ENGINES. 265
fire-box and the tubes of the boiler. It will then
be at once perceived that, for a given surface of
tubes^ there needs a certain draught, that is, a
certain aperture of the blast-pipe, to carry the flame
to the very extremity of the tubes, so that the
whole of their extent may receive the direct action
of the flame. This result once obtained, a greater
contraction of the blast-pipe or stronger draught,
could only have the effect of carrying the flame
beyond the extremity of the tubes, that is, into the
chimney, where it would no longer influence the
quantity of water vaporized. Diminishing, then,
the orifice of the blast-pipe still more and more,
beyond this point, would produce no change at all
in the vaporization of the boiler, if the extreme
contraction of the blast-pipe would not render at last
the passage of the air through the fire-box so rapid
that the greater part of it traverse the fire without
being used for the combustion. This is an eflfect
which manifested itself in our experiments; for
during those which took place with a blast-pipe
of r25 square inch of area, every stroke of the
piston caused in the chimney a violent noise, some-
what resembling the report of a gun. It is readily
conceived, then, that the contracting of the blast-
pipe beyond certain limits, is productive of no ad-
vantage to the vaporization of the engine.
As to enlarging the blast-pipe too much, since
it then ceases to supply a sufiicient draught in the
fire-box to carry the flame to the extremity of the
266 CHAPTER X.
tubes, the remaining portion of these, beyond the
point where the flame reaches, receives only the heat
communicated by the contact of the hot gases re-
sulting from the combustion already terminated;
and the definitive vaporization must thereby be
diminished.
This latter case carried to the extreme, would at
last considerably reduce the vaporization, and con-
sequently the eflfect of the engines; and this in-
deed is observed in practice, when a locomotive has
been made with too large a blast-pipe, or when the
latter has been corroded and widened by the effect
of the fire ; but as these defects are easily recognised
and corrected, they are to be regarded only as
momentary and exceptional. Hence, in the calcu-
lation of the effect of locomotives, we need consider
but small variations in the diameter of the blast-
pipe; and in such case, then, we see by the pre-
ceding experiments, that the change resulting in the
vaporization of the engine is not. of such importance
as to require being introduced into the general
formulae of the motion of these engines.
Sect. V. Of the comparative vaporization of the
fire-box and the iubeSy and of the definitive vapor-
ization of the engines per unit of heating surface of
their boiler.
We have just inquired into the particular in-
fluence, which divers circumstances may have on
OF THE VAPORIZATION OF THE ENGINES. 267
the vaporization of the engines : it now remains to
examine the effects which may result in that respect
from the construction of the boiler itself, or from
the proportion that has been established between
the heating surface of the fire-box and that of the
tubes. We shall first seek then, how much of the
total vaporization produced is attributable to each
of these two portions of the boiler, and thence we
shall afterwards conclude the definitive vaporization
of the engines per unit of heating surface of their
boiler.
The boiler of locomotives consists, as we have
seen, of two distinct portions, one of which sur-
rounds the fire-box, the other contains the tubes.
The water contained in the portion which surrounds
the fire-box, is every where in contact either with
the ignited fiiel, or with the flame which rises above
that fuel. The water which surrounds the tubes,
on the contrary, according to the intensity of the
fire, and the length of the tubes, may be in con-
tact, throughout the length of the tubes, either
with the flame, that is to say, the ignited gases
which issue from the fire-box, or partly with the
flame and partly with the hot gases which are
produced by the combustion. Now it is easy to
conceive that the effect of the tubes will be very
different in the two cases which we have just men-
tioned. If the tubes are in contact with the flame
throughout their length, it does not appear that,
comparing equal surfaces, they ought to produce
268 CHAPTER X.
a vaporization less considerable than the fire-box ;
for the ignited gases which traverse them, are
fuel as well as the coke itself, and it may be said
that throughout their length they receive the im-
mediate and radiating action of the fire. But if the
combustion slackens in the fire-box, so that the
flame extend only half-way along the tubes, that
portion alone of the tubes will be really submitted
to the radiating action of the caloric, and the rest
will receive no more than the communicative heat
arising from the contact of the still hot gases re*
maining after the combustion has ceased. Thus, in
this case, the first half of the tubes may, with equal
surface, produce as much vaporization as the fire-
box, but the second half will necessarily produce a
less effect, whence results that the mean vaporiza-
tion of the tubes, per unit of their total surface,
will then be less than that of the fire-box.
In a series of experiments which we undertook in
1836, at the station of the Liverpool and Man-
chester Railway, with Mr. Edward Woods, the
Company's engineer, on a boiler originally made
for a locomotive, but used in a stationary engine,
and in which the two compartments were separated
by a partition, — a circumstance which admitted of
measuring directly the vaporization produced by
the fire-box and by the tubes, — we, in fact, obtained
results analogous to those which have just been in-
dicated. The boiler was very long, and when the
fire was left to itself, and the vaporization not
OF THE VAPORIZATION OF THE ENGINES. 269
abundant, the tubes produced, comparing equal
surfaces, an effect considerably less than the fire-
box ; but by degrees, on the combustion being more
excited, and especially when, by means of a blast-
pipe taken from an adjacent boiler, a more violent
jet of steam was applied to the urging of the fire,
the effect of the tubes differed less and less from
that of the fire-box. As these experiments have
not been quite conclusive, we shall not report them
here, as to the precise results ; but we mention the
tendency of those results, in order to explain how,
in an experiment on the same subject, an English
engineer, operating on a small model, at rest, and
without using the blast-pipe, could obtain for the
proportion of the effect of the fire-box, to that of
the tubes, the ratio of 3 to 1 ; and how, on the
contrary, during the activity of the motion, with
engines of the usual dimensions, and with the use
of the blast-pipe, the two portions of the boiler may,
if they are not too disproportionate one to the other,
produce, per equal surface, equal effects, as we are
about to see that it results from the preceding ex-
periments, for the engines submitted to trial.
Referring, in effect, to the Table of page 253, in
which the engines are divided into series, according
to the proportions existing between the fire-box and
the tubes, we perceive that, in the first and second
series, the total heating surface is about 6' 5 times
that of the fire-box ; in the third series, it amounts
to 8' 7 times that of the fire-box ; and in fine, in the
270 CHAPTER X.
fourth series, the total surface is but 4*5 times that
of the fire-box. If then there were a considerable
difference between the effect of the fire-box and that
of the tubes, it would be found that in the engines
wherein the fire-box forms a larger portion of the
total sur£aboe, the eflect produced per unit of surface
would be greater. But, on the contrary, if we ob-
serve the means deduced fix)m the last three series,
we find that notwithstanding the diversity of pro-
portion between the fire-box and the tubes, the
vaporization per square foot of total heating surface
remains always sensibly the same. We must then
conclude, that during the active working of engines
of a construction similar to that of the experiments,
the two portions of the boiler vaporize, per unit of
surface, the same quantity of water.
To know the vaporization of which a given engine
is capable, it consequently suffices to measure the
number of square feet composing its total heating
surface, without distinction between the fire-box and
the tubes, and then to multiply that number by the
vaporization which each square foot of surface is
capable of producing. It is then the latter quantity
which we must now seek to determine ; but, as we
have seen that the vaporization produced per unit
of surface varies with the velocity of the motion, it
is necessary to specify at the same time the velocity
at which we wish to measure the vaporization.
Now, referring to the experiments of page 253,
we find that in the engines of the second series, the
OF THE VAPORIZATION OF THE ENGINES. 271
vaporization per square foot of heating surface was
•198 cubic foot, at the velocity of 18* 15 miles per
hour. On the other hand, we know that the va-
porization varies in the direct ratio of the fourth
roots of the velocities. We may then deduce from
thence, that at the velocity of 20 miles per hour,
the vaporization of those engines will be
/ 20 \i
• 198 Vi815/ ~ '^^^ cubic foot of water per
square foot of heating surface.
Operating in the same manner for the two following
series, we obtain, for the velocity of 20 miles per
hour, the determinations of the following Table.
Experiments on the vaporization of locomotive engines, per
unit of total heating surface of their boiler.
Nrnnber of
the series.
Average velo-
city of the en-
gine, in miles
per hour.
Vaporization per hour
and per sq. foot of total
heating surface, at the
preceding velocity.
Vaporization per hour
and per sq. foot of total
heating surface, at the
velocity of 20 miles
per hour.
miles.
cubic foot.
cubic foot.
2nd,
1815
•198
•203
3rd,
2013
•200
•200
4th,
8-99
•172
•210
4th,
15-26
•194
Mean
•208
. . -205
Thus, from these experiments, it appears that at
the velocity of 20 miles per hour, the vaporization
J
272 CHAPTER X.
of locomotives may be valued at 205, or, in round
numbers, at '2 cubic foot of water per hour, per
square foot of total heating surface of their boiler ;
and it appears also that the different engines and
different velocities lead to numbers almost identical,
which tends to confirm the valuation we have just
obtained.
This determination is, as we have said, suitable to
the velocity of 20 miles per hour ; but it is easy to
deduce from it that which would take place at any
other velocity, by multiplying by the fourth root of
the ratio between the given velocity and the velocity
of 20 miles.
Such then will be the vaporization of an engine
in motion, or, more properly, of an engine in which
the blast -pipe is used. But if the engine is stopped,
and the action of the blast-pipe interrupted in con-
sequence, the first series of experiments presented
page 253, proves that the vaporization per unit of
heating surface then reduces itself, on an average, to
•037 cubic foot of water per hour, that is to say, to
about a fifth of what it is at the velocity of 15 or 20
miles per hour. Thus, it will be possible, in all
cases, to estimate the quantity of water reduced to
steam by a given engine, in a determined time.
It is to be remarked, that were the vaporization
of engines considered as composed of two parts,
namely, the vaporization at rest, which is constant,
plus a variable augment depending on the velocity ;
it would then be deduced from the preceding ex-
L
OF THE VAPORIZATION OF THE ENGINES. 273
periments, that this variable portion changes in the
ratio of the cubic roots, and not in that of the
fourth roots of the velocities. But as, in reality, it
is not the absence of velocity in the engine, but the
interruption of the action of the blast-pipe, which
produces the observed decrease of vaporization,
during the moments of rest of the engines, it ap-
pears more accurate to consider these two effects of
the engine, with or without blast-pipe, as entirely
distinct from each other. Thus we will say that
the engine, at rest or in motion, but without blast-
pipe, vaporizes about 037 cubic foot of cold water
per hour, per square foot of total heating surface ;
but that, the action of the blast-pipe once intro-
duced and regulated by the velocity, the vaporization
will vary according to the fourth root of the latter,
and that at the velocity of 20 miles per hour, the
vaporization will be '205 cubic foot of water per
hoiu*, per square foot of total heating surface.
It must however be observed, with respect to
these determinations, that they are strictly suitable
only to boilers constructed in proportions not very
different from those used in the experiments ; that
is to say, according to what has been explained
above, that the heating surface of the fire-box ought
not to be under a tenth of the total heating surface
of the boiler, and the orifice of the blast-pipe not
much larger than we had it in our experiments,
according to the adopted practice. Were any
notable change made in this respect, were the coke
T
\
274 CHAPTBR X.
of an inferior quality, or the engine materially dif-
ferent in construction fix)m what we have described,
there would be grounds for a new determination
of the vaporization.
In fine, we will again add, that the numbers ob-
tained above indicate rather the consumption of
water of the boiler, than the real vaporization pro-
duced ; for we shall presently see, that out of the
total water thus expended by the engine, there is a
portion which is drawn into the cylinders, mixed
with the steam, but without being itself vaporized.
Consequently, to obtain the real vaporization of the
engine, it will be necessary to take account of this
circumstance, as we shall do further on.
Sect. VI. Of the loss of steam which takes place by
the safety-valves^ during the work of locomotive
engines.
Among locomotive engines there are a great
number which are subject to a continual loss of
steam by the safety-valves. This effect arises from
the engine being designedly constructed with an
excess of power ; that is to say, that according to
the production of steam which takes place in its
boiler, the engine could draw its regular load at a
greater velocity than it is allowed to do. The result
is, that to prevent the engine from acquiring too
great a velocity, it becomes necessary partially to
close the regulator, that is, to diminish the passage
1^
OF THE VAPORIZATION OF THE ENGINES. 275
of the steam, till no more enters the cylinder than
the quantity necessary to produce the desired ve-
locity. Then the surplus accumulating in the boiler,
at last raises the safety-valve and escapes into the
atmosphere. When this loss takes place only on
the regulator being somewhat closed, it is but a
proof, as we have said, of a surplus of power which
the engine holds in reserve. But if it takes place
more or less under all circumstances, then it de-
pends on the steam-ways being too narrow, and is
consequently a defect in the engine ; in either case,
however, it is necessary to obtain a valuation of
this loss.
There is yet another case in which engines are
subject to a loss of steam by the valves ; but this
loss is owing to a different cause fix)m the preceding,
and exhibits itself much more abundantly: it is
when the engine ascends a steep accUvity, with an
apparently moderate load, or when it ascends a
moderate inclination, with a very heavy load. At
these moments the valves are always seen to emit
an enormous quantity of steam. The reason is that,
as soon as the engine reaches the inclined plane, its
load instantly becomes extremely heavy, on account
of the surplus of traction required by the gravity on
the plane. It has been shown, in effect, that on a
plane inclined iho^ every ton produces, by gravity
alone, a resistance equal to that of 3*7 tons on a
level. It happens therefore, at that moment, that
the resistance of the train may become greater than
i^
276 CHAPTER X.
the actual pressure of the safety-valve. Conse-
quently the steam, instead of flowing by the cylinder,
driving back the piston, raises the safety-valve, and
escapes into the atmosphere. If then the passage
which the steam thus opens for itself were sufficient
for its total efflux, no more steam would pass
through the cylinder, and the engine would in-
evitably stop. But we have already said, in speak-
ing of safety-valves, that they are held in place by a
spring which exerts a resistance by so much the
greater as it is more compressed. The si^ety-valve
then, being raised by the steam, acquires more and
more pressure, and thus there will occur a point
when that pressure becomes sufficient to keep the
train in motion on the plane. The steam at this
moment is free to escape at once by the safety-valve
and by the cylinder, and divides itself between the
two issues, in proportion to the orifices ofiered by
them. Consequently the motion of the train then
continues, but on condition that the steam shall
preserve this accidental pressure ; that is to say,
that the valve shall still remain at the same point
of elevation, or in fine, on condition that a con-
siderable portion of the steam shall be lost in the
atmosphere. This loss might be greatly diminished,
by momentarily increasing the pressure of the
safety-valve, so as to put it in equilibrio with the
resistance which the train on the inchned plane
produces against the motion ; but as it might
happen, if the engine-men were allowed this facility,
i
OF THE VAPORIZATION OF THE ENGINES. 277
that they would use it inconsiderately and to the
detriment of the engine, a collar is usually fixed
on the rod of the spring-balance, which hinders the
nut from being tightened beyond a certain point.
This loss therefore is inevitable, whenever the de-
finitive resistance produced by the train exceeds the
extreme pressure thus fixed on the engine.
We are now about to consider in turn the two
wastes of steam of which we have just spoken.
To obtain some estimation of the quantity of
steam which escapes by the safety-valve, during
the regular work of locomotives, we had recourse
to the following method. During the whole con-
tinuance of the experiments on vaporization, which
we have just presented, we noted the point at which
the valve began to rise, and carefully observed the
mean point at which it stood by the effect of the
blowing of the steam. The interval between these
two degrees gave the rising of the valve during the
experiment, a rising in virtue of which the issue of
the steam took place. Thus it will presently be
seen that in experiment XII., the valve of the
Vesta, fixed at 20 degrees of the balance as the
starting point, rose on an average to 21*3 degrees
by the blowing of the steam. The rising of the
valve, or the passage constantly opened to the
steam, during the experiment, was therefore 1*3
degrees measured on the balance.
On the other hand, when the regulator of the
engine was designedly closed, the whole of the
278 CHAPTER X.
Steam generated in the boiler was forced to escape
by the safety-valve. Observing then how many
d^rees the valve rose, we could recognise the
nnmber of d^rees which corresponded to the total
production of steam in the boiler. Comparing then
the first rising with the second, that is to say, the
partial opening of the valve, which took place in
the regular work of the engine, with the opening
capable of allowing the total issue of the steam, we
could estimate the loss under consideration, as a
portion of the total steam produced in the boiler.
In the following Table we have collected the ob-
servations made on this head, first during the expe--
riments on vaporization already given, and after-
vrards while the r^ulator was totally closed. With
respect to the number of d^rees which represent
the total issue of the steam in difierait engines, it
will be conceived that this number depends firstly
on the quantity of steam produced by each boiler ;
again, on the diameter of the valve, which, for a
same degree of rising, may allow a greater or less
passage to the steam; then on the dimensions of
the levers and the size of the divisions of the
balance, which make a d^ree of that balance cor-
respond to a more or less considerable rising ; and
lastly, on the state of the second safety-valve of the
engine, which may itself give more or less issue to
the steam, or may not give it issue at all.
OF THE VAPORIZATION OF THE ENGINES. 279
Experiments on the habitual waste of steam which takes
place by the safety-valves of locomotive engines, during
their regular work.
Number
of the
experiment.
Nttneofthe
engine.
Rising of the valve,
in degrees of the
balance, observed du-
ring the experiment.
Rishig of the valve, in de-
grees of the balance, suf-
ficient to give issue to the
totality of the steam formed
during the complete dose
oif the regulator.
XII.
Vksta.
1-3
3-5
XIII.
FiRBFLT I.
0
3
XIV.
•7
3
XV.
Fury.
1-5
5
XVI.
—
1-4
5
XVII.
Lrxdb.
1-2
5
XVIII.
—
20
5
XIX.
Vulcan.
1-5
5
XX.
Atlas.
•7
4
XXI.
—
•1
4
XXII.
1-5
4
11-9
46-5
From this Table it is seen that the rising of the
valve which took place in the experiments was, in
degrees of the balances, 11*9 out of 46*5, that is to
say, it amounted to nearly a fourth of the total
steam produced during the total close of the regu-
lator. Now, during the close of the regulator, the
steam produced by the engine no longer passes to
the cylinders, and consequently ceases to urge the
fire in the fire*box ; and we have seen that during
280 CHAPTER X.
the suspension of that artificial excitation of the
fire» the engine produces scarcely a fifth part of its
vaporization during the work. It is therefore to be
concluded from the preceding experiments, that in
the engines submitted to observation, the loss of
steam by the valves might be valued approxima-
tively at ^ of the total steam produced in the
boiler during the motion of the engine.
The loss which has just occupied our attention is
in some sort permanent during the work of the
engines, and among all those which we have sub-
mitted to experiment, the Star, whose passages for
the circulation of the steam are very large, is the
only one that was exempt from it. It will be ne-
cessary then to take account of this circumstance,
for all engines liable to it, during the whole con-
tinuance of the work of the engine.
As to the loss which now remains to treat of, and
which is occasioned in ascending steep acclivities, it
takes place in all engines; but it is merely acci-
dental, and need not be taken into consideration
except in calculations that may be relative to the
traversing of those planes. To obtain an approxi-
mate valuation of this loss, we used the same mode
as in the preceding research: we attentively ob-
served the engines of the Liverpool and Manchester
Railway, while ascending, without an auxiliary en-
gine, the planes of Sutton and WMstan, inclined ^
and ^, and the acclivity of Chatmoss, inclined iin^,
and noted the jising of their valves which took
OF THE VAPORIZATION OF THE ENGINES. 281
place. The following Table contains the result of
those observations, compared as before with the
rising capable of giving issue to the whole of the
steam produced in the boiler during the complete
close of the regulator.
Experiments on the (accidental loss which takes place by the
safety-valves of locomotive engines ^ while ascending planes
considerably inclined.
Name of
the engine.
engine.
Load of
theenginct
tender
included.
Inclina-
tion of
the
plane.
Velocity
of the
enjrine, in
muea per
hoar.
Rising of the
valve, in de-
grees of the
balance, ob-
served during
the ascent of
the plane.
Rising of the
of the balance,
sufficient to give
issue to the to-
talitv of the steam
proauced during
the complete close
of the regulator.
Vesta.
Fu»Y.
Fu»T.
Lkkds.
Vulcan.
Atlas.
Atlas.
tons.
8-71
8-20
8-20
7-07
8*34
11-40
11*40
tons.
33-15
48-80
56-16
3515
39-07
195-5
40-15
tAtt
miles.
14-11
15-00
6-31
10-00
11-42
8-00
7-50
2-50
4
3
I
5
1-75
2-50
3-5
5
5
5
5
4
4
19-75
31-5
From these experiments, it is visible that when,
by reason of an excessive load on a moderate in-
clination, or of an ordinary load on a steep acclivity,
the engines are called upon to work at a pressure
higher than that fixed by their safety-valve, they
are liable to a variable loss, but which here on an
282 CHAPTER X.
by the boiler during the close of the regulator. And
as we have shown that the latter vaporization is ^
of that which takes place during the action of the
blast-pipe, that is, during the progression of the
engine, the above loss may be represented by
19-75
31-5
Xi = i=-12
of the total vaporization produced by the engine
during its motion.
It is conceivable, however, that the extent of this
accidental loss must vary under different circum-
stances, and that it depends on the diameter of the
valves, the length of the levers, the elasticity of the
spring of the balance, and above all on the excess
of the momentary resistance of the train above the
pressure at which the safety-valve of the engine is
regulated. For this reason, in calculations wherein
precision is required, it will be necessary, as much
as possible, to take account of it from direct ob-
servation for every engine.
Sect. VII. Of the water draivn into the cylinders
in its liquid state^ and of the effective vaporization
of the engines.
There exists another loss much more important
than the preceding, and to which locomotive engines
OF THE VAPORIZATION OF THE ENGINES. 283
are particularly gubject, by reason of the continual
jerks which they undergo in their motion, of the
little elevation of the entrance of the steam-pipe
above the level of the water, of the small space
reserved to the steam for its accumulation, and of
the exceeding rapidity with which the steam issues
from the liquid in the boiler. This loss consists of
a considerable quantity of water drawn into the
cylinders in its liquid state, and mixed with the
steam, but without being itself vaporized. To con-
ceive how this effect is produced, it suffices to
observe the enormous quantities of water which are
held in suspension in the air, in the form of douds,
and borne about by the wind. As, moreover, the
steam which is produced in the boiler of locomo-
tives is of a density much greater than that of the
air, and as instead of touching merely the surface
of the liquid, it disengages itself from the very
middle of that liquid, one need not be surprised
that it draws along with it a very considerable mass
of water ; and this effect will naturally be produced
during the whole time of the work of the engine.
To obtain a valuation of the loss which occurs in
locomotives from this cause, we, either by aug-
menting the load, or by lowering the pressure, or
by choosing inclined portions of the road to tra-
verse, placed the engines in such circumstances that
the pressure of the steam in the cylinder could differ
but very little from the pressure in the boiler i and
we then compared the velocity really produced, with
284 CHAPTER X.
that which ought to have heen produced, had the
totality of the water expended by the engine been
really converted into steam. The difference between
the water corresponding to the actual velocity of
the engine and the total water expended during
the motion, showed the quantity of water carried
in its liquid state into the cylinders with the steam.
The cases in which the engine works at a pressure
in the cylinder sensibly equal to that of the boiler,
have already been pointed out; they are those
wherein the engine reduces its velocity till it be-
comes impossible to admit that the steam can
increase in volume, and consequently diminish in
pressure on entering the cylinder, since such an
increase of volume, slight as it might be imagined
to be, would necessarily bring with it a greater
velocity of the engine than the velocity observed.
Now in performing for the different experiments
which we are about to report, the calculation neces-
sary to compare the real velocity of the engine with
the velocity which ought to correspond to the total
expenditure of water of the boiler, it will be recog-
nised that in those experiments, the pressure of the
steam in the cylinder could not be sensibly less than
the pressure in the boiler ; and this fact will again
be found verified on performing, in the manner
developed in Chapter IX., the calculation of the
resistance then exerted by the load against the
piston, a resistance which we shall see equal to the
pressure of the steam in the cylinder.
OF THE VAPORIZATION OF THE ENGINES. 285
To show how the calculation has been performed
in the following experiments, we will give it in
detail for the first of them. In this experiment, the
engine Atlas, expending 43*81 cubic feet of water
per hour, at the average velocity of 8*99 miles per
hour, assumed on an inclined plane and with a
considerable load, a velocity of 8*00 miles per hour,
working at a total pressure of 69*7 fts. per square
inch in the boiler. As the engine was then moving
only at 8 miles per hour, whereas its mean vapor-
ization of 43* 81 cubic feet of water had been
observed at the velocity of 8*99 miles per hour, and
as it has been shown that the vaporization of engines
varies as the fourth roots of the velocities, we see,
firstly, that its vaporization during the portion con-
»
sidered of the experiment, must have decreased to
42*56 cubic feet.
On the other hand, the safety-valve of the engine,
observed at the same moment, was raised 1*75
degrees of the balance, and in the engine Atlas,
an elevation of 4 degrees of the balance suflices, as
has been said above, to give issue to the whole of
the steam that the engine can produce while at
rest. The loss of steam by the safety-valve was
therefore
1^ = -4375
4
of the vaporization of the engine at rest. Now it
has been shown that the vaporization while at rest
is '037 cubic foot of water per hour, per square foot
286 CHAPTER X.
of total heating surface ; and referring to the Table,
page 37, Chapter I., we see that the total heating
surface of the Atlas is 254 '31 square feet. Hence
the loss of steam which took place by the safety-
valve during the ascent of the plane, was
•4375 X 037 X 254-31 =4- 12 cubic feet per hour.
Consequently the effective vaporization of the en-
gine, at the same moment, was
42-55 — 412 = 38-43 cubic feet per hour.
But since the pressure in the boiler, at the moment
of the experiment, was 69*7 fts. per square inch,
and the relative volume of the steam at that pres-
sure is 407 times that of the water, it is dear
in the first place, that admitting the steam to have
been expended in the cylinder at the pressure of the
boiler, which is the greatest pressure it can be
supposed to have, it would have produced a volume
of
407 X 38-43 =15641 cubic feet.
On the other hand, as the diameter of the cylin-
ders of this engine is 1 foot, and the stroke of the
piston 16 inches or 1*33 foot, the two cylinders
augmented by ^ for the vacant spaces filled by the
steam at each stroke, but not traversed by the
piston, offered a capacity of
2-199 cubic feet.
Such then was the volume of steam expended at
each stroke of the piston. But since the engine
OF THE VAPORIZATION OF THE ENGINES. 287
moved at a velocity of 8 miles or 42240 feet per
hour, with a wheel of 5 feet in diameter, '^r 15'71 feet
in circumference, it follows that it performed in an
hour 2689 turns of the wheel, and consequently
gave 5378 strokes of the piston in both the cy-
linders. The volume therefore of steam which it
expended was but
5378 X 2- 199 = 11827 cubic feet.
Now, we have seen that supposing the steam to
have had in the cyUnder the same pressure as in the
boiler, it would already have produced a volume of
15641 cubic feet, and every supposition of a smaller
pressure for the steam carries with it the necessity
of a volume still greater. Consequently, it is im-
possible to admit that the steam can have expended
itself in the cylinder at a lower pressure than in the
boiler.
Moreover, since, supposing even the steam in the
cyUnder at the same pressure as in the boiler, which
is the most favourable supposition we can make, it
still happens that the volume of steam expended
by the cylinder is less than the volume of steam
generated in the boiler, a part of the water must
have been carried from the boiler to the cylinder, in
its liquid state; and the comparison between the
quantity of water consumed by the boiler and that
which, in the state of vapour, corresponds to the ve-
locity of the piston, shows that the quantity of water
really converted into steam, is to the total quantity
of water consumed, in the ratio of the numbers
288 CHAPTER X.
15641
Thus, in this experiment, we see that '24 of the
water expended by the boiler was carried into the
cylinders without being reduced to steam, or that the
real vaporization of the engine was '76 of the total
water expended.
For the other experiments, we give in the fol-
lowing Table all the elements of the calculation,
which is performed in a manner entirely similar,
except that in the experiments made with the engine
Star, on the acclivity of r^o> ^^ blowing of the
safety-valve took place, which dispenses with intro-
ducing a reduction in that respect.
It will be observed that if, in any one of these
experiments, we had committed an error in admit-
ting that the pressure in the cylinder was the same
as in the boiler, it would then follow that the
quantity of water carried in its liquid state with the
steam, would have been greater than our determina-
tion gives it, for that experiment. Consequently,
we are siure that the result which we have obtained
is not exaggerated.
It will be remarked, again, that the loss here ob-
served in the engines, cannot be attributed to the
partial condensation of the steam in the steam-ways
and cylinders, because the position of these in the
smoke-box, where they are in continual contact
with the flame of the fire-box, renders that supposi-
tion quite inadmissible.
OF THE VAPORIZATION OF THE ENGINES. 289
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290 CHAPTER X.
These results make known the quantity of water
carried in its liquid state, with the steam, in the
engines submitted to experiment. When we shall
present (Chapter XII.) a series of obsenrations on
the velocity and load of locomotives, it will appear
that two experiments made with the engine Star,
on the plane inclined g^, would equally have fur-
nished, for that engine, a determination of the
quantity of water carried with the steam ; but as,
in these two cases, the risings of the valve took
place without being observed, and as it could have
been estimated only approximatively, we deemed it
proper to prefer the two expmments of the Table,
on the plane inclined nj^, because there was then
no loss by the valve, which removed all error in this
respect.
Among the engines which we submitted to ex-
periment, as will be seen further on, there are two,
the Firefly and the Leeds, in which we have not
been able to determine the quantity of water carried
with the steam. The reason of this is, that the
former being then in a bad state of repair, and
losing water by the tubes, was never in a condition
to work with a heavy load. As to the second, it
once ascended the plane inclined ^ with a load of
35' 15 tons, and must have worked at full pressure
in the cylinder ; but as this engine, when its r^u-
lator was quite open, was liable to prime consider-
ably, that is, to fill its cylinders with water in a
liquid state, and then to throw that water through
the chinmey in the form of rain, it was never made
OF THE VAPORIZATION OF THE ENGINES. 291
to work but with the regulator partially closed. On
the other hand, when ascending the plane inclined
^ , the regulator had been entirely opened, in order
not to impede the work of the engine. It was then
found to lose a great deal more water than in the
ordinary course of its work. This experiment, then,
could only determine the quantity of water carried
in a liquid state, in an exceptional case, and not in
the regular working state of the engine. The other
en^es not being liable to the effect we have just
mentioned, did not offer the same difficulty.
The results which have just been presented above
show that the quantity of water carried away with
the steam, varies in different engines, and ought to
be determined for each separately ; but as, in taking
the means between the different experiments, that
loss is found to amount to '24 of the total vaporiza-
tion of the boiler, this proportion may be adopted
approximatively for engines that have not been
directly submitted to experiment in this respect;
that is to say, in order to have the effective vapor-
ization of a locomotive, the total vaporization of
which its boiler is capable, must be first measured ;
from the result must be subtracted, if necessary, the
loss, either accidental or permanent, which may be
observed at the safety-valves, and the remainder
must be multiplied by the fraction 76. Thus will
be obtained the volume of water which passes into
the cylinder, in the real state of steam, and produces
the motion of the piston.
292 CHAPTER X.
average determination may serve for engines
not submitted to the experiment, as the Leeds and
the Firefly ; but for those which have been the ob-
ject of a particular determination, the latter ought
of course to be employed, because the quantity of
water carried with the steam evidently depends on
the peculiar construction of each engine, and espe-
cially on the space reserved for the steam to form and
accumulate in the boiler. If, in effect, that space is
but ten times the capacity of the cylinder, it is clear
that, at every stroke of the piston, a tenth of the
steam generated will pass into the cylinder, and the
density of the remaining steam will thus be found
all at once reduced to nine-tenths of what it was
before. This great change of density will immedi-
ately demand from the liquid, a new quantity of
steam to replace that which is gone ; but it is evi-
dent that the new steam will emerge from the Uquid
with so much the more violence, and consequently
will draw by so much the more of that Uquid with
it, as it shall rush into a more rarified medium. If
then the space reserved to the steam in the boiler
contain 100 cylinders-full of steam, instead of 10,
as the difference of density produced at each stroke
of the piston will be but y^, instead of |^, the
quantity of water carried away with the steam will
be by so much less considerable. This is a fact well
known in practice; for engines are observed to be
much more liable to prime when the boiler is full,
than when it is moderately filled. In locomotive
OF THB VAPORIZATION OF THB ENGINES. 293
engines, the space left to the steam for its formation,
consists of the top part of the boiler, and what is
called the steam-dome. Clearly then, a boiler too
small, or a steam-dome too confined, tends to aug-
ment the effect under consideration.
Moreover, if the entrance of the steam-pipe is
but little elevated above the surface of the water
of the boiler, and if it has a large diameter, the
result must naturally be, that the steam will the
more easily be raised to the entrance of the pipe,
and be received into it in greater abundance. This
is why some engines are subject to priming when
their regulator is quite open, which depends on the
orifice of the regulator ; and were the inquiry as to
the quantity of water carried with the steam sus-
ceptible of sufiicient precision, it is probable that in
all engines that quantity would be found somewhat
greater in the cases wherein the regulator is entirely
open, than in those wherein it is but partially so.
The quantity of water carried with the steam
must then vary according to the peculiar construc-
tion of the engines ; but it is yet again influenced
by circumstances independent of the construction.
Thus, when a very active fire is made in the fire-
box, as there is then produced in the boiler a very
considerable vaporization for the quantity of water
it contains, and as, in consequence, there results a
current of steam, through the liquid, by so much
the more violent, it is conceivable that the water
294 CHAPTSR X.
carried with the steam must augment at the same
time. In like manner, fouhiess of the water, form-
ing at the surfiBU^ a scum which the steam blows
and traverses continually, must produce a similar
effect ; and, in fine, the higher the pressure in the
boiler, the more easily the steam must carry the
liquid water with it.
From what has just been seen, the carrying away
of water in a liquid state takes place in the engines
without any external sign of it being manifested,
because the water mixed with the steam dissipates
itself with it in the air. But there are moments
when this effect is so violent, that it exhibits itself
externally in a very evident manner. This occurs
when the boiler is too full, or when, in order to set
the engine in motion, the regulator is opened sud-
denly, instead of being opened by degrees. At such
times is seen inmiediately to fall from the chinmey
an actual rain, which in practice is expressed by
saying that the engine is priming. In the first case,
the quantity of water carried with the steam evi-
dently proceeds from the diminution of the space
left to the steam for its formation. In the second,
it proceeds from the opening of the regulator giving
all at once a considerable issue to the steam, whilst
the cylinders and pipes are then but sUghtly warm,
and filled with a steam extremely rarified. The
steam at that moment accumulated in the boiler
is therefore in a manner carried off suddenly, and
OF THB VAPORIZATION OF THB ENGINES. 295
in the agitation caused by the rapid formation of
the new steam, a great quantity of water is carried
with it.
The extent of the loss which, has just occupied
our attention, explains how some boilers expend
water so rapidly that it is impossible to keep them
fiilly even at a very moderate velocity, and how it
has sometimes happened that by merely changing
the steam-dome of an engine, a considerable re-
duction has been made in its expenditure of fuel.
For this reason there is room to think that as the
construction of locomotives shall advance towards
perfection, this loss will diminish, and consequently
the consumption of fuel which attends it will di-
minish at the same time. It is however to be
observed, that the loss of fuel resulting from this
defect is not in proportion to the loss of water
itself; because the latter being carried off from the
boiler in a state of liquid, carries with it only the
sensible beat indicated by the temperature of the
boiler, whereas, the rest of the water being carried
off in the state of steam, carries with it, besides, the
latent heat necessary to its existence in the state of
an elastic fluid.
CHAPTER XL
OF FUEL.
Sect. I. Experiments on the consumption of fuel ne-
cessary to produce^ in locom4)tive engines, a given
vaporization.
Bkfore passing on to the calculation of the effects
of locomotives, there is still another element of that
calculation which it is indispensable to consider;
namely, the quantity of fuel necessary to produce,
in locomotive engines, a given vaporization.
In order to arrive at the determination of this
element, during the experiments presented above,
and which had for their object to make known the
vaporization of the boiler, we carefully noted also
the corresponding quantity of fuel consumed. To
that end, the tender was first completely emptied of
all the remaining fuel, the coke then accurately
weighed and put into the tender. The fire-box
was besides filled with coke to the level of the lower
part of the door. At the end of the experiment,
the fire-box was filled anew to the same height, and
what coke remained in the tender was weighed with
the same care as before starting.
In all the experiments the fuel employed was
OF FUEL. 297
coke of the best quality, or Worsley coke, which
is prepared expressly for foundries. When the
engines use that which is obtained from the gas-
works, they consume about 12 per cent, more, ex-
clusively of the loss arising from the friability of
that fuel. It has moreover been found that the
sulphurous parts contained in it are particularly de-
structive to metals, and for that reason the Liver-
pool and Manchester Railway Company have com-
pletely renounced the use of it, notwithstanding its
moderate price. The smoke emitted by the com-
bustion of coal prevents its being usually employed
in locomotives, and therefore we have made no re-
searches as to the use of that fuel.
The experiments of which we are about to give
the results were made on the Manchester and Liver-
pool Railway. To take account of the delays which
occurred on the road during the trip, and of the de-
scent of the inclined planes with the regulator shut,
we employed the same method as for the vaporiza-
tion. That is to say, since experience shows that
the consumption of fuel in the engines, while at rest
or without the action of the blast-pipe, is about the
fifth of their consumption while in motion, we have
replaced the time of suspension of the action of the
blast-pipe by the fifth of that time, which we have
then added to the time of the effective progression
of the engine ; and it is by the total time thus found
that we have divided the fuel expended, to deduce
therefrom the consumption of fuel per hour qf
motion.
298
CHAPTER XI.
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OF FUEL. 299
In examining these experiments, it will be proper
first to distinguish the efiects of the introduction of
the blast-pipe itself, .from the effects which are
afterwards due to the more or less contraction of it.
The first three experiments, which were made
without the application of the blast-pipe, prove that
the fuel consumed per hour in a locomotive engme
in which the waste steam is not employed to excite
the fire, and consequently in a locomotive engine at
rest, is but about a fifth of the consumption which
takes place in the same engine, during the use of the
blast-pipe, or during the progression of the train.
This is the fact which we have just made use of to
take account of the stoppages of the engines.
As soon as the blast-pipe is employed, the con-,
sumption of fuel per hour in the fire-box augments
considerably, and consequently the corresponding
vaporization. But comparing the first and second
series of the preceding experiments, we perceive
that the vaporization produced does not augment
quite so fast as the consumption of fuel. In effect,
in the second series, the ratio between the surface
of the fire-box and the total heating surface ia
nearly the same as in the first series. There is
room then to think, from what will presently be
seen, that the consumption of fuel per cubic foot of
water vaporized, would have been nearly the same
in the two series, if the second had not taken place
with the use of the blast-pipe. Whereas, we find
that the consumption of fuel, which was only 9 9>s.
300 CHAPTER XT.
of coke per cubic foot of water iu the first case,
amounted in the second to ITSfts. Hence we
must then conclude that the introduction of the
blast-pipe greatly aids the combustion, but that the
definitive vaporization produced by the engine does
not augment in an equal proportion ; and we shall
presently see the reason of it, viz., that when the
consumption of fuel mcreases by the introduction
of the blast-pipe, the heating surfieu^, remaining the
same, no longer preserves the same proportion with
the quantity of fuel consumed.
Thus, at first, we see that the introduction of the
blast-pipe leads to the result of increasing the con-
sumption of fuel per hour in the fire-box, and
likewise the vaporization of the boiler, though in a
less proportion. But in seeking afterwards the in-
fluence of a greater or less contraction of the blast-
pipe, we cannot clearly distinguish any very marked
effects in that respect. There is room to think
that the consumption of fuel per hour, at equal
velocities of the engine, must be increased to a
certain degree by the contraction of the blast-pipe,
as we have said in treating of the vaporization;
but this augmentation appears too slight to show
itself in a decided manner. It is easily found com-
pensated by accidental circumstances, of which it is
impossible accurately to take account, such as the
quality of the fuel employed and the care of the
engine-man in stoking the fire ; and we see defini-
tively that, in practice, and regarding only the usual
OF FUEL. 301
variations of the blast-pipe, we may consider the
consumption of fuel per hour as undergoing no
sensible change with the size of the blast-pipe.
Sect. II. Of the most advantageous proportion to
establish between the fire-box and the tubes of the
boiler^ in locomotive engines.
It is still to be remarked in the preceding Table,
that the diiferent engmes are more or less econo-
mical with regard to fiiel, in proportion to the
corresponding vaporization ; that is to say, they do
not all consume the same quantity of fuel to pro-
duce the same vaporization. With this in view, we
have divided the engines into several series, accord-
ing to the ratio which exists in each of them between
the heating surface of the fire-box and that of the
tubes, or, which comes to the same, between the
heating surface of the fire-box and the total heating
surface of the boiler. In the engines of the first
and second series, the total heating surface is about
6 '5 times that of the fire-box ; in the third series, it
amounts to 8*7 times that of the fire-box ; and in
fine, in the fourth series, the total heating surface is
but 4*5 times that of the fire-box. The means
deduced from each series of experiments show the
motive of this division ; for, comparing them to-
gether, we form the following Table.
302
CHAPTER XI.
Experiments on the most advantageous proportion to be
established between the fire-box and tubes, in locomotive
engines.
Nnmhcr
of the
•erica.
Average heetuiK sur&ce
Vaporisa-
tionper
hour.
Cokeeon-
samedper
hour.
Ratio between
the total heating
■urfkce, and that
of the fire-box.
Coke per
cubktoot
of water
vaporised.
of the
fire-box.
dfthe
tube*.
IV.
II.
III.
Bq. feet.
57-07
49-30
36-74
sq. feet.
197-25
272-15
282-09
cub. feet.
47-34
63-47
63-70
lbs.
551
715
583
4-46
6-52
8-68
!b8.
11-65
11-31
918
We see by this Table that the consumption of
Aiel per cubic foot of water vaporized, is so much
the less as the total heating surface offers a greater
extent relatively to the fire-box ; and this result is
easily accounted for on observing that the less fuel
is consumed in an engine whose heating surface
does not vary, the more heating surface there is
per pound of fuel consumed, and consequently the
more completely absorbed by the liquid is the ca-
loric developed by each pound of fuel. Thus, in
the third series, the fire-box was of such dimensions,
that the engine consumed only 583 9>s. of coke per
hour, whereas in the engines of the second series,
the fire-box could consume 715 lbs. of coke in the
same time. On the other hand, in each of the two
series the total heating surface offered to the action
of the fire was nearly the same, namely, 320 and
321 square feet. The caloric developed by each
OF FUEL. 303
pound of coke was then received by a surface of
f5J.==.45 square foot in the second series, and of
f|^= -55 square foot in the third ; which explains
the advantage of the latter on the score of economy.
It is for the same reason likewise, that, in the first
series, the engines without blast-pipe, though of
similar proportions to those of the second series,
have yet been more economical in their expen-
diture, because the absence of the blast-pipe having
rendered the consumption of fuel, in those engines,
less considerable for a like heating surface, the case
became similar to that of the third series compared
to the second.
Finally, a like effect is again recognisable in the
comparison of the third and fourth series. In the
latter, the quantity of fuel consumed was not greater
than in the third series ; . but the heating surface
exposed to receive the action of the fuel was only
254 square feet instead of 320 ; and a corre-
spondent difference of economy has resulted for the
production of the steam.
We may then at once conclude from what pre-
cedes, that the most economical locomotive engines
are those whose heating surface is the greatest rela-
tively to the consumption of fuel in the fire-box ;
and as, in the same system of construction of fire-
boxes, and with the use of the blast-pipe, the con-
sumption of fuel, that is, the capacity of the fire-
box, may be regarded as sensibly proportional to its
heating surface, it is visible that the most eco-
304 CHAPTER XI.
Domical locomotive engines, with respect to fuel, are
those in which the total heating surface is greatest
relatively to that of the fire-hox.
From this remark, one should then be induced to
increase more and mcHe the surface of the tubes
relatively to that of the fire-box ; there would, in
effect, be thus obtained a still greater and greater
economy of fuel : but there is another condition yet
more important in the use of locomotive engines
than the saving of fuel ; and that is, to produce the
greatest possible quantity of steam with a boiler of a
given size. Now, it is evident that by more and
more augmenting the surfece of the tubes, we should
bring them at last to such an extent that the flame
of the fuel could cover only a portion of them.
Hence, from what has been said (Chapter X.), the
vaporization of the boiler, per unit of heating surface
would lower at the same time.
This, in fact, is what is observed on the Great
Western Railway. There are engines, on that line,
in which the total heating surface is equal to 10*3
times that of the fire-box, and others in which the
ratio between those two surfaces is carried so fiBu: as
11 '3 and 11*6. In the first, the consumption of
coke is 8'801bs., and in the second, 8*43 lbs. per
cubic foot of water vaporized. But at the same
time, the vaporization of the first, referred to the
velocity of 20 miles per hour, is '200 cubic foot of
water per square foot of heating surface, as in the
engines of the Table which we have presented
OF FUEL. 305
above, whereas in the second, the vaporization, re-
ferred to the same velocity, is no more than '185
cubic foot of water per square foot of total heating
surface. It is clear then that, in the latter, the
saving of fuel is obtained only at the expense of the
effect of the engine, whereas with the proportion of
about 10*3 between the total heating surface and
that of the fire-box, the expenditure of fiiel is di-
minished, without the definitive vaporization of the
engine undergoing any reduction.
These different effects are easily accounted for by
the observations we have already made in treating
of the vaporization ; but we will dwell yet a moment
on the subject, to endeavour to recognise what is the
most advantageous proportion to establish between
the heating surface of the tubes and that of the fire-
box.
When the surface of the tubes amounts to but
about 3 or 4 times that of the fire-box, as in the
engines of the fourth series of our experiments, the
engine consumed as much as ir65fts. of coke per
cubic foot of water vaporized, because the excess of
coke burnt in the fire-box serves only to carry the
flame beyond the extremity of the tubes, that is to
say, into the chimney, where it ceases to influence
the vaporization, and can produce no other effect
but to destroy rapidly the parts of the engine with
which it comes in contact. Increasing then the
surface of the tubes to 8 or 9 times that of the
fire-box, as in the engines of the third series, the
x
306 CHAPTER XI.
consumption of coke is reduced to 9'18!bs. of coke
per cubic foot of water vaporized, without the de-
finitive vaporization of the engine being affected,
because the change has done no more than remedy
the loss of fuel above mentioned. Finally, by aug-
menting the surface of the tubes beyond 10 times
that of the fire-box, a further reduction is obtained
in the expenditure of fuel per cubic foot of water va-
porized ; because not content with employing merely
the flame which rises from the fire-box, we turn
to use also a part of the caloric carried with the
gases resulting from the combustion effected. But
the portion of the tubes which serves to utilize this
latter portion of caloric, produces much less vapor-
ization than the rest of the boiler, whence results
that the definitive vaporization of the engine, per
unit of total heating surface, is found reduced at the
same time.
We have reason then to think, firom the difierent
experiments cited above, that with coke for fuel,
and with the other circumstances of the work and
the construction of the engines, the most advan-
tageous ratio to estabUsh between the total heating
surface and that of the fire-box, would be nearly that
of 10 to 1 : since for a less proportion there would be
increase in the expenditure of fuel, without increase
of vaporization; and for a greater proportion, on
the contrary, there would be reduction in the
vaporization of the engine per unit of surface,
which would incur the necessity of a larger boiler,
OF FUEL. 307
and consequently of a greater weight, which it is
important to avoid.
In fine, to arrive at a general conclusion from the
experiments which we have presented above, it ap-
pears that, according to the proportion of the fire-
box to the total heating surface, the consumption of
fuel in locomotive engines varies from 92 to 11*3
and 11*7 lbs. per cubic foot of total water vaporized ;
so that it may, on an average, be valued at
10'7fts. of coke, per cubic foot of total
vaporization.
Sect. II. Of the consumption of fuel necessary to
draw a given load a given distance.
The result which we have just obtained makes
known the average quantity of coke consumed, in
the engines submitted to experiment, to produce a
determined vaporization ; but what is necessary to
be known, in practice, is the quantity of fuel neces-
sary to draw 1 ton a mile. Specif)dng in each of
the experiments above noticed, and in some others
which we are about to add to them, the load then
drawn by the engine, and taking account of the dis-
tance which that load was conveyed, we form the
following Table, in which is seen the consumption
of coke per ton per mile, which took place in each
case.
In this Table we first give the weight of the load,
the duration of the trip, and the delays which oc-
308 CHAPTKR XI.
corred on the road ; and as the liyerpool and Man-
chester Railway, on whidi the experiments were
made, has, in each direction, besides divers less
important acclivities, an indined plane on which
it is often necessary to have assisting engines, we
give also the number of those engines which were
employed to draw the trains to the top of the
planes inclined ^ and ^. We afterwards give
the pressure of the steam in the boiler, and the
velocity of the motion. The following column
shows the consumption of coke which took place
during the experiment, first such as it was ob-
served, that is, delays included, and then delays
deducted. To make this deduction, we proceed
as it has been explained in the preceding section,
that is to say, we add to the real duration of the
trip the fifth of the delays, and by the time thus
calculated we divide the total consumption of fuel,
in order to obtain the consumption of coke which
took place per hour or per minute, during the
activity of the motion. Then, as soon as we know
the consumption of ftiel per minute of active mo-
tion, we take the fifth of it, which gives the con-
sumption of ftiel of the engine per minute of rest ;
after which it is easy to conclude that which takes
place during the delays. Consequently, in fine, sub-
tracting this from the total consumption, we obtain
the numbers inserted in the eleventh column.
From what has just been explained, we have all
the elements of the experiments. Nothing remains
OP FUEL. 309
but to determine the quantity of work, in tons con-
veyed 1 mile, which has been executed in each case ;
and dividing the consumption of fuel, delays de-
ducted, by the quantity of work done, we have the
consumption of fuel per ton per mile, such as it
is contained in the twelfth column. The following
need no explanation.
To obtain the quantity of work performed by the
engine in each case, we refer the reader to Sect. vi.
Chapter XVII. It will there be seen that, by reason
of the different inclinations which exist on the Man-
chester and Liverpool Railway, in order to obtain
the quantity of work requisite for the draught of a
train along the whole line, the following formulae
must be used, according as the train is going from
Liverpool to Manchester, or from Manchester to
Liverpool, and according as the passage of the in-
clined plane is performed with or without assisting
engine :
From Liverpool to f without assisting engine 30*79 M, + 206
Manchester \ with assisting engine 30*79 M^ + 318 ;
From Manchester f without assisting engine 36*89 M, + 292
to Liverpool \ with assisting engine 36*89 M^ + 404.
In these formulae, Mi expresses the load of the en-
gine in tons gross, tender not included; and the
constant number added to each expression, repre-
sents the quantity of work consumed by the friction
of the tender of the engine, and by the gravity of
the engine and its tender, on the different acclivities
of the line. In the case of assisting engines, the
310 CHAPTBR XI.
constant number comprises moreover an addition
of 112 tons conveyed 1 mile, which represents the
gravity of the assisting engine and its tender, and
the friction of that tender itself, on the inclined
plane traversed by the engine.
These formulae gave then the total work per-
formed by the trip engine and the assisting en-
gine united, for the conveyance of the train upon
the line. But if it be desired to know the work
done by the trip engine, taken separately, then,
from each of the foregoing expressions, must be
subtracted the work done by the assisting engine.
Now, as this engine is always more powerful than
the trip engine, it may be estimated that, during
the common action of the two engines, that is,
during the passage of the inclined plane, the as-
sisting engine, over and above its own weight and
that of its tender, draws f of the load Mi.
On the other hand, we have said that the weight
of the assisting engine and its tender consumes,
during the ascent of the plane, a quantity of work
expressed by 1 1 2 tons conveyed 1 mile on a level ;
and, recurring to Sect. vi. Chapter XVIL, it will be
found that the ascent of the load M, on the inclined
plane, causes, with regard to Ifriction and gravity, a
quantity of work represented by 7*18 M, tons 1
mile, f of which are 4*79 M| tons 1 mile. The
total work performed by the assisting engine is
therefore represented by
479 M, + 112.
OF FUEL. 311
Finally then, subtracting, for the cases of assisting
engines, this quantity from the preceding formulae,
we have, for the quantity of work done by the trip
engine, taken separately :
From Liverpool to f without assisting engine 30" 79 M, -f 206
Manchester \ with assisting engine 26*00 M , + 206 ;
From Manchester f without assisting engine 36*89 M, -f 292
to Liverpool \ with assisting engine 32*10 M^ -f 292.
The result of these formulae gives, in tons gross
conveyed 1 mile, the work executed by the engine
during the total trip along the line. By this result
then ought to be divided the quantity of coke con-
sumed by the engine, delays deducted, to conclude
the consumption of coke per ton conveyed 1 mile.
Performing this calculation, we find the numbers of
the thirteenth column of the Table.
312
CHAPTER XI.
ExperimefUs on the quantity ofjwl consumed
Number
of theex-
pcnuMut>
VI.
IV.
V.
VII.
VIII.
X.
IX.
XI.
XXIII.
XII.
XXIV.
XXV.
XIV.
XIII.
XV.
XVI.
XVII.
XVIII.
XXVI.
XIX
XX
XXVII.
XXI.
XXVIII.
XXIX.
XXX.
XXXI.
XXXII.
XXII.
XXXIII.
Dftteofthe
cxpenniMit.
Aug. 9,
Aug. 13,
Aug. 9,
Aug. 9,
Aug. 11,
Aug. 13,
Aug. 11,
Aug. 10,
July 5,
Aug. 1,
July 16,
July 16,
July 26,
July 26,
July 24,
July 24,
Aug. 15,
Aug. 15,
July 1,
July 22,
July 23,
July 9,
Aug. 4,
July 14,
July 11,
June 28,
July 16,
July 17,
July 31,
July 17,
836.
836.
836.
836.
836.
836.
836.
836.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
834.
Name of the engUw,
and place of ttarCing.
Stab, from Uy.
' from —
— from Man.
— from liv.
from Man.
' from —
^— from LiY.
' from —
Vbsta, frt>m liT.
— from Man.
JupiTBE, from Man.
— from Liv.
FiRBFLT,from Man.
— from liY.
FnmT, from Man.
-^— from liv.
L»D8, frt>m LiY.
—^ from Man.
Vulcan, from liv.
—^ from Man.
Atlas,
from Liv.
from —
from —
fix)m -^
from — •
from —
from -^
frt>m —
from Man.
frx>m —
Natnre and wdght
of the load, in
jitMay tcadaf
not indiidad.
23 wag.
22vrag.
35 wag.
20 wag.
15 wag.
9 wag.
12 wag.
12 wag.
tons.
114*77
104-18
69-55
90*80
55-74
42-98
54-34
38-15
20 wag. 92-75
10 wag. 28*15
7 coach. 30-09
8 coach. 33-09
8 coach. 36-40
8 coach. 36-40
10 wag. 43-80
10 wag. 51-16
20 wag. 83-34
8 wag. 32*01
20 wag. 97-70
9 coach. 34*07
40 wag.
25 wag.
25 wag.
25 wag.
25 wag.
25 wag.
20 wag.
15 wag.
12 wag.
13 wag.
19000
123-13
122-64
118-90
117-61
113-90
94-66
65*40
35-15
25-30
Duiaticn ol
the trip,
delaya not
indttdad.
h. m.
1
2
2
57
8
15
42
41
S4i
37i
25i
42
H
12
12
18
35
35
30
35
17*
37
17
2
48
58
31
41
50
25
27
54
26
DelM*
OB the
mad.
mm.
15
11
3&
36
22
5
15*
13
5
0
4
3
5
5
0
0
0
3
3
3
15
12
0
19
5
5
23
3
0
3
Nnnber of
aatistin^
lO
theindined
plaoei.
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
2
3
(t
ft
2
1
0
0
OP FUBL.
313
by locomotive engines, in drawinff given loads.
AvvfSfe
Coke eoDsomed
Coke
Coke per
Arerefe
velocity
of the
during the trip,
oon-
siuned
per hour,
ton gross
drawn cme
mile one
State ef the
water in the ten-
fffectiTe
presrare
in miles
deUya
delays
deUys
level, ten-
der, at the
in the
PV
ID-
de.
de-
der not
starting of the
State of the
boUer.
Aoor.
dnded.
ducted.
ducted.
indoded.
engine.
weather.
Obsenrationa.
lbs. per
miles.
Its.
Hw.
Am.
fbs.
84). in.
38-7
15-13
1369
1322
708
-41
Almoat cold.
Fair and calm.
34-3
13-85
1431
1398
666
•48
Cold.
Fair and calm.
rss empty wag.
45-1
14-45
1456
1358
652
•54
Very hot.
Fair and calm.
^ —The engine
ascended the
LplaneinStoms.
35-8
17-35
1409
1302
805
-51
Hot.
Fair and calm.
?»
17-46
1248
1182
741
-57
Cold.
Fair and calm.
0 wag. empty.
270
18-79
920
900
603
•54
Hot.
Pair and calm.
26-3
18-32
nil
1064
690
•66
Tepid.
Fair and calm.
23-5
20-78
1133
1084
809
•90
Hot.
Fair and calm.
53
17-35
916
897
555
•34
Hot.
«Blm.
51
27-23
774
761
761
•57
Very hot.
Fkir, wind fav.
S wag. empty.
53
24-58
836
812
727
•65
f»
Fair, wind agst.
53
24-58
742
721
645
•68
Almost cold.
Pair and calm.
49
21-33
870
847
696
•58
Tepid.
Rainy, wind agst
/The engine in
\ a bad state.
44
17-70
879
858
639
-75
Almost cold.
Fkir.
57
18-63
746
738
492
•39
Cold.
Fair, w. sideways.
57
19-67
806
797
562
•45
Cold.
Fair and calm.
54
18-63
897
887
592
•37
Hardly tepid.
Fair and calm.
_ A ■ •« .a
49
21-99
690
675
560
•46
Very hot.
F^ and calm.
/ 1 wag. half the
iroad.
54-5
18-25
1071
1048
684
•38
Tepid.
Calm.
54-5
22*99
664
650
541
•42
Hazdly tepid.
Fair, wind agst.
53-7
8-99
1596
1561
529
•30
Cold.
Cahn.
53
16-39
1102
1071
624
•31
Tepid.
ff
r Wheel con.
necttng-rods
. too tight.
53
15-00
1224
1213
644
•36
Cold.
Fair and calm.
61-5
19-45
1118
1057
737
-32
Cold.
Pair and calm.
53
17-53
1136
1113
696
•34
Tepid.
ft
53
1609
1104
1084
619
•34
Rather hot.
tt
53-5
20-82
1081
1005
754
•38
Bather tepid.
Calm.
54
20-35
1012
988
723
•52
Very hot.
Fair and calm.
30
15-53
881
873
481
•55
Cold.
It
4 wag. empty.
54-5
20-58
720
703
520
-57
Very hot.
Pair and calm.
8 wag. empty.
314 CHAPTER XI.
Examining these experiments, we immediately
recognise that the quantity of coke necessary to
draw a ton 1 mile, is so much the greater as the
load of the engine is less, or as the velocity is
greater. We recognise at the same time, that
this effect is not owing to an increase in the con-
sumption of fuel per hour ; for that consumption
does not appear to undergo any regular change ;
the variations we observe in it, sometimes in ex-
cess, sometimes in diminution, being sufficiently
explained by some accidental difference in the
quality of the fuel, or in the assiduity of the
engine-man in stoking the fire. But the difference
noticed here is easily accounted for, on considering
that the engine is obliged, besides its load, to draw
its own weight and that of its tender, and to over-
come divers constant resistances ; and the quantity
of fuel necessary to perform this work being then
divided according to the number of tons in the
load, becomes by so much the more sensible as
the load itself is lighter. Thus it is that we see
the same engine expending twice and almost three
times as much coke, per ton per mile, in one experi-
ment as in another.
It would therefore be inaccurate to draw an average
result from the preceding Table, in order to apply
it to the different cases that might occur. But if it
be desired to know the quantity of fuel necessary
for the engine per ton per mile, the load the engine
is to draw must previously be given. Now, by
OF FUEL. 315
measuring the heating surface of the boiler, and
recurring to the results obtained in Chapter X., the
quantity of water which the engine is able to va-
porize per hour will be known ; and consequently,
from the experiments presented in Section i. of
the present chapter, the corresponding consumption
of fuel will be deduced. Then, by the formulae
which will be developed in Chapter XIL, the ve-
locity of the engine with the given load on any
inclination whatever will be determined. There-
fore, if the railway in question be level, or if it
consist of one uniform inclination, in multiplying
the given load by the velocity the engine will
assume with that load, the product will immedi-
ately make known, in tons conveyed 1 mile per
hour, the useful effect of the engine. Dividing
then the consumption of fuel of the engine per
hour, by the useful effect produced in the same
time, the quotient will give definitively the quantity
of fuel which will be consumed by the engine, per
ton per mile, in drawing the given load. This
method will be a natural consequence of the very
theory of the engine, as will be seen in Chapter
XIL, when we come to treat of the useful effect
of locomotive engines, and for this reason we shall
not dwell any longer upon it here.
If the railway in question, instead of being es-
tablished on a uniform inclination, be composed
of a series of ascents and descents, the velocity
of the engine must be calculated on each of the
316 CHAPTBR XI.
inclinatioiis ; and, by the process indicated in Sect.
III. Chapter XVII., the total time of the trip will
be determined. Consequently, since the consump-
tion of fuel per hour is already known, that which
will take place during the whole duration of the trip
will immediately be concluded. Then, proceeding,
as we have just done, to form the foregoing Table,
or as will be explained Sect. ti. Chapter XVII.,
the work executed by the engine during the same
trip will be obtained. Dividing then the expendi-
ture of fuel by the work executed, the result will
definitiyely be the quantity of coke, per ton per
mile, expended by the engine, in drawing the given
load, on the variously inclined railway in question.
CHAPTER XII.
THEORY OF LOCOMOTIVE ENGINES.
ARTICLE I.
OP THB EFFECTS OF THE ENGINES WITH AN INDEFI-
NITE LOAD OR VELOCITY.
Sect. I. Of the different problems which present
themselves in the calculation of the effects of loco^
motive engines.
The principal problems which occur with respect
to locomotive engines have reference in the first
place to two circumstances, namely: I. When the
engine is already constructed, and the question
is to determine the effects that it wiU produce;
II. When the engine is as yet unbuilt, and the
question is to determine the proportions it ought
to have in order to produce desired effects. At
present we consider only the questions relative to
the first case, and shall reserve the others for the
following -chapter.
When an engine is already constructed, and all
its dimensions may be directly measured, the fol-
lowing problems may present themselves:
318 CHAPTER XII.
1st. To determine the velocity the engine will
assume, with a fixed load ;
2nd. To determine the load it will draw at a
desired velocity;
3rd. To determine the usefhl effect it will pro-
duce, at a desired velocity or with a fixed
load.
And this last problem may, itself, he expressed
under ten different forms, namely, to find suc-
cessively :
The useful effect of the engine, in tons drawn
1 mile;
The useful effect expressed in horse-power ;
The quantity of fuel necessary per ton per mile ;
The quantity of water necessary per ton per mile ;
The useful effect produced per pound of fuel con-
sumed ;
The useful effect produced per cubic foot of water
vaporized ;
The consumption of fuel which produces 1 horse-
power;
The consumption of water which produces 1 horse-
power ;
The horse-power produced per pound of fuel ;
The horse-power produced per cubic foot of water
vaporized.
Moreover, as two cases are necessarily to be dis-
tinguished in the work of the engines, namely, the
case in which they work with a load or velocity
indefinite, and that in which they work with the
OF THE EFFECTS OF THE ENGINES. 319
load or velocity which produces the maximum of
useful effect, there will yet occur in this respect a
new series of questions, namely :
1st. To determine the velocity at which the
engine will produce its maximum of useful
effect ;
2nd. To determine the load corresponding to the
production of the maximum of useful eflFect ;
3rd. To determine the maximum of useful effect
that the engine can produce.
And this last problem may be expressed under the
ten different forms which we have indicated above.
We will, then, consider successively these two
series of questions.
Sect. II. Of the elements to be considered in the
calculation of the engines.
In the attempts hitherto made for calculating the
effects of steam engines, or for determining the ve-
locity of the piston under a given load, the cal-
culation has been grounded on two data only : the
pressure of the steam in the boiler, and the re-
sistance of the load against the piston.
This mode seems to comprehend all the data of
the problem ; but its erroneousness ought to have
been recognised, when it was seen that all essays
made to arrive at any formulae by this means,
produced nothing that was not annihilated by ex-
perience. It is more especially in endeavouring to
320 CIIAPTBR XII.
apply this method or these formulae to the motion
of locomotive engines, in order to determine the
load they can draw at a given velocity, or the
velocity they can assume under a given load, that
the calculator is quickly led to results which are
palpably inadmissible.
The cause of this appears in these two facts : 1st.
That the pressure of the steam in the boiler, even
supposing it to represent exactly the pressure in the
cylinder, or the effort applied against the piston,
would be far from offering, on that account, a
complete measure of the power of the engine, that
is to say, of the motive force of which it can dispose,
and could not therefore be sufficient to calculate its
effects : 2nd. That the pressure in the boiler does
not represent the pressure in the cylinder, or the
effort appUed against the piston, but can only fix its
extreme limits, that is to say, it can only indicate
the maximum load of which the engine is capable,
and nothing else. We shall here demonstrate the
first of these points ; the second will naturally be
made clear when we come to treat of the pressure
in the cylinder.
We say, that supposing the case wherein the
pressure in the cylinder were equal to the pressure
in the boiler, that is, the case in which, on mea-
suring the pressure in the boiler, we should thereby
obtain the effort applied by the engine, that measure
would not suffice to make known its disposable
motive force, nor consequently to calculate the
OF THE EFFECTS OF THE ENGINES. 321
effects it can produce. In fact, when we consider
201 engine in a state of statical equilibrium, or at
rest, the force which it applies reducing itself to
a simple pressure, is found completely represented
by the effort which the engine can exert, or by the
mass which it can hold in equiUbrium. But when
we consider engines in a state of motion, the force
which they apply is no longer a pressure, but a
motive force ; that is to say, it is no longer Umited
to the producing of an effort, but an effort and a
velocity. ITiis force, therefore, is no longer mea-
sured by the mass which it can hold in statical
equilibrium, but by the mass which it holds in
d3mamical equilibrium, that is, in uniform motion,
and by the velocity which it is capable of com-
municating to that mass. If then the effect of a
steam engine were to be calculated in the state of
equilibrium at rest, it might be sufficient to take
account, in the calculation, of the pressure of the
steam, which would make known the intensity of
the effort applied ; but as, on the contrary, it never
occurs to compute the effects of these engines,
except in a <6tate of motion, it follows, that to
estimate the motive force of which they can dispose,
or to calculate their effects, we must at once take
account of the effort applied by the engine, and of
the velocity with which it can maintain that effort.
Now, in steam engines, the pressure of the steam
indicates only the mass which the engine can hold
in equilibrium, and it is the velocity of the production
Y
322 CHAPTER XII.
of the steam alone which indicates the velocity
which the engine can communicate to that mass.
Hence it is only hy introducing these two elements
into the calculation, that an exact valuation can be
attained of the effects which will be produced.
The velocity of production of the steam is nothing
more than the quantity of steam generated in a
given time. Thus, the power of an engine resides
at once in the greater or less quantity of steam
which it produces, and in the degree of pressure
or elastic force of that steam. In this valuation,
the pressure is visibly no more than the means of
verifying the state of the force, at the moment
when in a manner its quantity is measured; and
this explains why, in the statical equilibrium, that
is, when no velocity is produced, and it therefore
becomes useless to consider that quantity, the
pressure suffices to represent the power; but it m
otherwise in the state of motion, because then, as
we have seen above, the pressure of the steam is but
one of the elements to be considered.
We may besides obtain conviction, by more prac-
tical considerations, that the pressure of the steam
in the boiler cannot suffice to determine the velocity
of the engine with a given load. If, in effect, a loco-
motive engine be put to trial, weak as it may be on
the score of vaporization, it is easy, by loading the
safety-valve with 50fts. per square inch, to fill the
boiler with steam at that effective pressure, or,
which means the same, at the total pressure of 65fts.
OF THE EFFECTS OF THE ENGINES. 323
per square inch. If then a load of 100 tons be
attached to the engine, let which be the greatest
load it can draw with an effective pressure of 50]bs.
per square inch, will it be said that the engine must
necessarily draw that load at a certam fixed velocity
which shall depend only on the pressure in the
boiler and the resistance to the piston ? Certainly
not ; for if it happen that the engine transform per
minute 1 cubic foot of water into steam at the
pressure of the boiler, it may, by that vaporization,
produce a certain velocity ; but if it vaporize but
half that quantity, ceteris paribus, it clearly can fill
the cylinder but half the number of times per
minute. Thus the pressure in the boiler may
remain the same ; but the velocity of the engine,
with the same load, must necessarily be reduced to
half. It is plain, then, that the pressure in the
boiler does not suffice to represent completely the
power of the engine, or to make known its effects.
But if, by analogy with other boilers already
tried, and by a comparison of the extent of heating
surfaces, we previously estimate what quantity of
steam, at a given pressure, a boiler is able to pro-
duce per minute ; or if, with still more efiicacy, we
fill the boiler with water, and producing in the fire-
box, by any means whatever, a fire as intense as it
is in the usual work, we ascertain its vaporizing
power; then alone we shall know the velocity at
which the engine can continue its motive effort.
324 CHAPTER XII.
and be able to estimate the work it can perform
in a given time.
The pressure of the steam in the boiler, taken
alone, can determine but one thing: viz., the limit
of the load of the engine, from the necessity which
exists that the resistance against the piston should
never exceed the pressure in the boiler, since the
resistance would then be greater than the power,
and consequently the motion could not be produced.
But in every inquiry into which the velocity figures,
recourse must necessarily be had to the vaporizii^
power ; and then the separate influence of each of
these two elements in the result is this :
The limit of the load possible for the engine is
given by the degree of pressure in the boiler ;
And the velocity with that load, or with any
other, is given by the vaporizing power.
These effects will become much clearer as we
shall develope the theory of the engine; but we
thought it right to explain them here in a summary
way, to show from what motive we entirely lay
aside the ordinary mode of calculation applied to
steam engines. Since the first edition of this work,
we have published, under the title of Tlieory of the
Steam Engine, a work in which we have developed
at length the proofs of the inaccuracy of the pro-
cesses in use for calculating the effects or the pro-
portions of steam engines ; to that work then we
refer for whatever may not appear to be sufiiciently
explained here.
OF THE EFFECTS OF THE ENGINES. 325
Sect. III. Of the pressure of the steam in the
cylinder.
The pressure of the steam in the cylinder is the
first inquiry that must engage our attention in order
to be able to determine the effects of the engine.
It is, in fact, always easy to ascertain the quantity
of steam generated per minute in the boiler. If
then we knew also the pressure at which that steam
is expended in the cylinder, we might immediately
conclude the velocity which the engine must neces-
sarily assume; for it would sufiice to divide the
volume of steam produced, by the contents of the
cylinder, to have the number of cylinders-fiill of
steam, and consequently the number of strokes of
the piston the engine will furnish per minute, which
will give its velocity.
At a first glance, it is natural enough to think
that the pressure of the steam in the cylinder must
be the same as in the boiler, or at least that it must
differ from it only according to the losses to which
the engine may be liable ; but it is easy to obtain
conviction that such is not the case, and that in an
engine subject to no loss of any kind whatever, the
pressure in the cylinder, during the permanent
motion, may at times be sensibly equal to that of
the boiler, and at times much less ; which depends,
not on losses supported by the steam, but on the
load drawn by the engine.
326 CHAPTER XII.
We know, in fact, that in every sort of engines
the velocity, exceedingly small at first, increases by
degrees up to a certain point, beyond which it does
not go, because the mover is not capable of greater
velocity with the mass which it has to move. If
the engine is well constructed, and especially if it is
regulated by a fly-wheel, that velocity, once at-
tained, maintains itself without alteration, though
the action of th^ mover may continue to vary, or,
in other words, to oscillate between certain limits,
and the motion becomes quite uniform.
As soon as the motion has attained uniformitv,
which always happens at the end of a short time,
and which is the normal state of the engine during
its work, the mover, which at the commencement of
the motion 'must necessarily have exerted a force
greater than the resistance, now expends but the
force precisely capable of holding that resistance in
equilibrium ; for were it to apply a force greater or
less, the motion would be accelerated or retarded,
whereas by the fact it is uniform.
Now, in the engines under consideration, the
force applied by the mover is nothing more than the
pressure of the steam against the piston, or in the
cylinder; as soon, therefore, as the engines have
attained uniform or permanent motion, the pressure
of the steam in the cylinder is strictly equal to the
resistance of the load against the piston.
To account for the manner in which the equi-
librium of pressure establishes itself in a locomotive
OF THE EFFECTS OF THE ENGINES. 327
engine, it suffices to trace its effects from the origin
of the motion. At that moment, the steam being
enclosed in the boiler at a certain pressm^, passes
into the steam-pipes, and thence into the cylinders.
Entering these, whose area is about 10 times that
of the pipes, the steam at first dilates, losing propor-
tionally its elastic force ; but as the piston is not
yet in motion, and as by reason of the load which it
supports, it can acquire its velocity but very slowly,
whereas the steam continues to arrive with rapidity,
the equilibrium of pressure quickly establishes itself
between the boiler and the cylinder; and the piston,
driven by all the force of the steam, begins slowly
to move in the cylinder. The motion thus im-
pressed on the piston communicates itself therefore
to the engine and to all its train, and the entire mass
acquires a certain velocity. At this moment, if
the arrival of the steam were suddenly intercepted,
the piston would not stop on that account; it
would, itself, be carried on for some time by the
force which it has previously communicated to
the moving mass. The result therefore is, that
at the following stroke, the steam finds the piston
already moving with a certain velocity, at the mo-
ment when it comes to impress a new quantity of
motion thereon; and this new supply of motion
passes on to the mass, where it continues to accu-
mulate. Thus, receiving at every stroke a fresh
impulse, and preserving the former one, the piston
by degrees accelerates its motion, and the train at
328 CHAPTER XII.
last acquires all the velocity the engine is capable of
communicating to it.
From what has just been said, we see that at the
moment of starting, the slowness of the motion
allows the steam to acquire in the cylinder the
same pressure as in the boiler, and that it is the
superiority of that pressure over the resistance of
the piston which makes the latter more and more
accelerate its motion, till at last it attains all the
velocity which it is capable of acquiring with the
resistance with which it is loaded. But as the
piston assumes a greater velocity, it in a manner
flies before the steam, without allowing it time to
acquire in the cylinder all the pressure it might
assume there. The action of the steam to ac-
celerate the motion of the piston, becomes then
less and less; and finally, when the piston has
attained the greatest velocity the engine can com-
municate to it, the accelerating action of the steam
upon it has become null, since it can augment its
motion no more. Now, the accelerating action of
the steam consists in the excess of its pressure above
that of the resistance. Hence at this moment the
pressure of the steam in the cylinder and that of the
resistance against the piston, are precisely in equi-
librium with each other ; and if the motion of the
engine remains in a state of uniformity, it is because
the resistance which is exerted continually, and
would have for eflfect to retard the motion, is im-
mediately destroyed by an equal pressure from the
OF THE EFFECTS OF THE ENGINES. 329
mover ; whence results that the motion must con-
tinue the same without alteration.
In steam engines in general, the uniformity of
motion is produced by a fly-wheel ; but in locomo-
tive cingines, it is the mass of the train itself which
performs the office of a fly-wheel. This mass
receives and in a manner stores the quantities of
motion impressed by the mover in its moments of
greatest action, to restore them afterwards, when the
mover is in a moment of less force ; and it is from
the very difficulty of increasing or diminishing the
velocity of the mass, that the uniformity of motion
of the whole results. With respect to certain parts
of the engine, which, like the piston, for instance,
must necessarily vary in velocity during the time
of their oscillations, the uniformity of motion in
question is imderstood to mean an exact conformity
of time, such that at any point of one oscillation, the
velocity is precisely the same as it was at the same
point of the preceding oscillation ; so that if the
duration of one of these oscillations were taken for
the unit of time, the motion would be strictly
uniform.
We see then, from what precedes, that at the
commencement of the motion or at the starting of
the engine, the steam begins by acquiring in the
cylinder a pressure equal to that of the boiler ; but
that this state is but transitory, and that as the
velocity of the piston increases, the pressure in the
cylinder gradually lowers, till at last it becomes
precisely equal to the resistance of the load. This
330 CHAPTER XII.
equilibrium once established, the velocity of the
piston ceases to increase, the motion becomes uni*
form, and the steam continues to expend itself in
the cylinder at the pressure indicated by the re-
sistance.
Thus, we know the pressure at which the steam
expends itself in the cylinder ; and knowing also the
volume of the cylinder, we may conclude the abso-
lute expenditure of steam which takes place at
every stroke of the piston ; wherefore, comparing
this expenditure with the total mass of steam of
which the engine can dispose, we may without
difficulty deduce the velocity of the motion.
Sect. IV. Of the velocity of the engine with a given
load.
We have just said that with the elements which
we have at our disposal, we can determine the
velocity which an engine will assume in drawing a
given load.
Suppose, in effect, that a load of 50 tons gross,
tender included, be drawn up a plane inclined y^,
by an engine with 2 cylinders 1 1 inches in diameter,
stroke of the piston 1 6 inches, wheels 5 feet, friction
103 fts., total pressure of the steam in the boiler
65 lbs., or effective pressure 50 lbs. per square inch,
and, finally, vaporizing power nearly such as we
have found it for the average of the Liverpool and
Manchester locomotive engines, that is, 60 cubic
feet of water per hour, or 1 cubic foot per minute.
OF THE EFFECTS OF THE ENGINES. 331
We have already found above, Chapter IX., that
the total resistance opposed by that load to the
motion of the piston, in the case of this engine, is
48 lbs. per square inch, when the velocity is 20
miles per hour. If then we admit that the engine
will came near enough to that velocity, for the
valuation which we have made of the resistance of
the air and the pressure caused by the blast-pipe, in
the calculation, not to be very far from the truth,
we must conclude that, during the uniform or
permanent motion of the engine with that load,
the pressure of the steam, during its action in
the cylinder, will Ukewise be 48 lbs. per square
inch.
Now the quantity of water consumed by the
boiler amounts to 60 cubic feet of water per hour,
and we have shown in treating of the vaporization,
that out of that mass of water 75-hundredths only,
on an average, are really converted into steam, and
that the rest is merely carried away with the steam
into the cylinders, but in a liquid state. The
effective vaporization of the engine is then firstly
•75 X 60 = 45 cubic feet per hour, or
•75 cubic foot per minute.
This water is first transformed, in the boiler, into
steam at the total pressure of 65ft8. per square
inch ; but on passing into the cylinders it acquires
the pressure of 48 lbs. per square inch, and we
know that, in this change, the steam remains al-
332 CHAPTER XII.
ways at the maximum density for its temperature.
Its volume may then be determined by the Tables
which we have giv^i in Chapter 11., on the volume
of the steam formed under different pressures. Ac-
cording to these Tables, the volume of the steam
formed under the total pressure of 48flto. per
square inch, is 573 times that of the water which
produced it. Hence the quantity of water efiec-
tively vaporized per minute in the boiler, will form
during its passage through the cylinders, a volume
of steam expressed by
573 X -75 = 430 cubic feet.
On the other hand, the area of each cylinder is
95 square inches, or in square feet that area is
represented by '66 square foot; and the stroke of
the piston is 1 6 inches or 1 '33 foot. Whence the
capacity of each cylinder, traversed by the piston, is
•88 cubic foot.
But, besides the portion traversed by the piston,
there still exists, at each end of each cylinder, a
vacant space called the clearance of the cylinder ^
which is necessarily filled with steam at each
stroke. Tlie capacity of this vacant space, re-
presented by an equivalent portion of the cylinder,
and steam -ways included, is usually ^ of the part
of the cylinder traversed by the piston. The real
capacity, therefore, which is filled with steam at
each stroke of the piston, is
OF THE EFFECTS OF THE ENGINES. 333
•88 X f^ = -924 cubic foot.
Consequently the number of strokes of the piston
which the engine will give per minute, by reason of
its effective vaporization, will necessarily be
430
•924
= 465.
Now each time the wheel makes one revolution,
the engine gives two strokes of the piston in each of
its two cylinders ; and the diameter of the wheel is
5 feet, which makes 15*71 feet in circumference.
Therefore at every 4 strokes of the piston, the
engine advances 15' 71 feet; that is to say, its
velocity, in feet per minute, will be
465
-|-X 15-71 = 1822 feet.
Fmally, as 1 mile contains 5280 feet, and 1 hour
contains 60 minutes, the definitive velocity of the
engine, in miles per hour, will be
60
■^^ X 1822 = 20-71 miles.
Thus we see that the above vaporization will ne-
cessarily produce a velocity of 20*7 miles per hour
for the engine ; that is to say, a locomotive engine
with the given proportions may, if in good order
and with a well-stocked fire, draw a load of 50 tons
gross, tender included, up a plane incUned 7^, at
the velocity of 20*7 miles per hour.
We shall, in the sequel, refer again to the pre-
334 CHAPTER xir.
vious valuation of the velocity of the engine, neces-
sary to have the resistance of the air against the
train, and to the variation of the vaporization. We
only wished, at this moment, to show the mode of
proceeding of the calculation.
With regard to the velocity which we have just
obtained, we must add, that if the engine suffers,
besides, a loss of steam by the safety-valve, which,
as we have seen, takes place in a great number of lo-
comotive engines, there will then be a corresponding
loss on the efiective vaporizaticm ; and consequently
the definitive velocity of the engine will be reduced
in a corresponding proportion. For instance, if the
engine, like those of the Liverpool and Manchester
Railway, be liable to a loss of *05 of its vaporization
in full activity, its definitive velocity, in the case
above mentioned, will become
•95 X 2071 = 19-67 miles per hour.
The calculation will be performed in the same
manner for every other load and for every other
engine. Thus, in general, resuming the notations
precedently employed, in the inquiry upon the re-
sistance on the piston, that is :
M, Representing the number of tons of the load,
tend^ included;
m. The weight of the engine, in tons ;
g. The gravity, in pounds, of one ton on the plane
the engine has to traverse ; this gravity being
null for the case of a horizontal plane ;
OF THE EFFECTS OF THE ENGINES. 335
k. The friction of the waggons per ton, expressed
in pounds;
xu The velocity of the engine, in miles per hour ;
uv^^ The resistance of the air against the train,
at the velocity t;, resistance expressed in
pounds;
p'v, The pressure against the piston, arising from
the action of the blast-pipe, expressed in
pounds per square foot ;
F, The friction of the engine, in pounds ;
S, Its additional friction, measured as a fraction of
the resistance, according to what was ex-
plained in Chapter VII. ;
D, The diameter of the propelling wheels of the
engine, in feet;
d. The diameter of the cylinder, in feet ;
/, The length of the stroke of the piston, in feet ;
c, The clearance of the cylinder, represented by
an equivalent portion of the stroke of the
piston, and consequently in feet ;
P, The total or absolute pressure of the steam in
the boiler, in pounds per square foot ;
jp. The atmospheric pressure, expressed in pounds
per square foot ;
Finally, S the effective vaporization of the engine,
in cubic feet of water per hour, at the ve-
locity known or unknown of the motion ;
D DF
R=(l+S)[(fc±5r)M±sfm+ui;'] ^+^57 +P+p'v
336 CHAPTER XII.
will be the pressure of the steam per unit of surface
in the cylinder, as has been demonstrated above,
Chapter EX.
On the other hand, if we express by /^ the rela-
tive volume of the steam generated under the pres-
sure R, a relative volume which will be found in
the Tables given Chapter 11. ; since S is the volume
of water vaporized per hour in the engine, it follows
that
will be the corresponding volume of the steam under
the pressure R, that is to say, during its action in the
cylinders.
But, expressing by ir the ratio of the circum-
ference to the diameter, the capacity of each cy-
linder which is traversed by the piston, has for its
measure
and the clearance of the cylinder offers, besides, a
capacity of
irrd^c.
Therefore the totality of the space filled with steam
at each stroke, in each cylinder, has for its ex-
pression
Consequently the number of strokes of the piston
corresponding to the volume of steam expended /i S,
will be
OF THE EFFECTS OF THE ENGINES. 337
/*=
But, while each piston performs 2 strokes, that
is, at every expenditure of 4 cyUnders-full of steam,
the engine advances 1 turn of the wheel, that is to
say, a space represented by
irD.
Therefore the velocity of the engine, in feet per
hour, will be expressed by the above number of
strokes, divided by 4 and multiplied by tt D ; that is
to say, the velocity will be
V — ^ ^
"■ d«" l+c'
And finally, as 1 mile contains 5280 feet, the velocity
of the engine, expressed in miles per hour, will be
v = J—. -^. -5- (1)
5280 d"" l+c
This expression will make known the velocity re-
quired, on substituting, for each of the letters, the
value suitable to it in the engine considered.
As it has been shown. Chapter II., that the rela-
tive volume of the steam under the pressure R, may
be expressed by
1
n + 5 R
it is plain that, instead of seeking the relative volume
fi in the Tables which we have given, its value may
be represented by the expression
1 ^ __J .
338 CHAPTER XII.
and consequently the preceding expression of the
velocity of the engine may equally be written under
the form
L. i J s (1 1,^3)
Such then will be the general expression of the
velocity of the engine, in miles per hour; an ex-
pression in which all is known from measures taken
on the engine, even the vaporization S, which re-
sults from the extent of heating surface, according
to what has been shown, Chapter X.
Making use of this formula to find the velocities
corresponding to divers loads of the engine, or to
divers values of M, attention must be paid never to
suppose, for M, a load capable of producing on the
piston a resistance greater than the pressure of the
steam in the boiler, because it is evident that the
resistance would then exceed the power, and the
motion could not take place. This maximum load
of the engine will form a special inquiry in Article
II. of this chapter. Nor can M be supposed of a
value less than the weight of the tender, which is
the minimum load an engine can have to draw.
Beyond these two limits the solutions given by the
formula would evidently cease to suit the problem.
As to the velocity resulting from this formula, we
shall equally see, in the following article of this
chapter, that, for a given value of the vaporization
S, it can never be less than a certain quantity which
we shall determine, and which will consequently
OF THE EFFECTS OF THE ENGINES. 339
make known the minimum velocity of the engine.
With respect to the maximum velocity that the
engine can attain, it clearly will depend principally
on two things; the weight of the load, and the
inclination of the plane on which that load is
drawn. If we first suppose either an ascending
inclined plane, or a horizontal plane, or an inclined
plane descending, but on which the gravity does
not exceed the friction of the train, it wiU be found
that the less the load is, the greater velocity the
engine will assume. If we suppose, on the con-
trary, a descending inclined plane, on which the
gravity exceeds the friction of the train, it will be
found that the more the plane is inclined, and the
heavier the train is, the more the velocity of the
motion will increase, because the excess of the
gravity above the friction will be by so much
more considerable, and that this force acts in
favour of the motion. But it is not to be supposed
that on a plane exceedingly inclined, or with a very
heavy load, the velocity of the motion can ever
increase indefinitely. The slightest essay of cal-
culation on the preceding formula will immediately
demonstrate this ; and the reason of it will readily
be conceived, on observing that by degrees as the
gravity and the efibrt of the engine tend to augment
the velocity of the train, the air opposes, on the
contrary, more resistance, and a resistance more-
over which increases in the ratio of the square of
the velocity. We shall see, therefore, Chapter
340 CHAPTER XII.
XVII., that the engines^ when descending inGlined
planes, assume much more moderate velocities than
one would be tempted to admit at a first view.
It is to be remarked that the formula which we
have just obtained for the velocity of the engine,
still contains, in the second member, the two terms
uv^ and p'v^ which are functions of v, and whose
value cannot consequently be precisely found with-
out knowing the velocity v itself, which is the
quantity sought. Were it desired to disengage the
unknown quantity entirely, those two terms must
be eliminated from the second member of the equa-
tion ; but to avoid the equation of the third degree
which would then result, the formula may be used
such as it is. In order to eflfect this, a probable
estimation must first be made of the quantity r, and
by means of it an approximation of the two terms
uv^ and p'v will be furnished ; then substituting
these in the formula, a certain value of v will be
deduced. If this value coincide with that which
has been supposed to determine the two terms
uv^ and p v, or at least differ from it only in an
inconsiderable degree, it will be the true value of
V, since it will completely satisfy the equation. If,
on the contrary, the value of v thus found differ too
much from that which has been supposed in the
determination of uv^ and p'v, for these two terms to
be considered as having been properly estimated,
the value of v obtained by this first calculation must
be employed, to estimate with more precision the
OF THE EFFECTS OF THE ENGINES. 341
two terms uv^ and p'v ; then, substituting them in
the equation, a second value of v will be attained,
more approximate than the first. This second
value, should it not appear sufficiently exact, would
serve in the same manner to find a third ; but with
a little practice in the calculation, two trials will
always be found sufficient, and the recurrence of
the same numbers will so simplify the research,
that a third trial, in case of need, will be made
without the least difficulty.
K it be wished to take account in the calculation
of the variations which the vaporization of the
engine undergoes by reason of the velocity, ac-
cording to what has been shown. Chapter X., the
given vaporization will be that which is known for a
certain determined velocity, that is, it will be, for
that velocity, the value of the quantity S then
supposed variable. In this case, the same process
must be used in determining S, as has just been
explained for the quantities p'v and uv^. Thus,
having made a previous estimation of the velocity,
the corresponding values of S, p'v and uv^ must be
deduced, and the equation solved with them. If the
resulting value of v do not coincide with the sup-
position made, the latter must be corrected, as has
been said above. This shall be illustrated further
on by an example.
We have yet to observe that the value of i;, in the
equation (1 bis), or the expression of the velocity of
the engine, is entirely independent of the pressure in
342 CHAPTER XII.
the boiler. This result has nothing suqprising ; for
we have proved that the steam assumes^ in the
cylinder, a pressure strictly indicated by the restst-
ance of the piston, and that moreover, in this
change, the steam remains at the maYimum density
for its temperature, as if it rose immediately from
the liquid at that very pressure. Hie consequence
is therefore, that it matters little whether the steam
has been originally produced in the boiler at any other
greater pressure, since that pressure in the boiler is
but a transitory state which ceases to subsist, and of
which no trace remains, as soon as the steam begins
its action. If, for instance, the resistance of the pis*
ton, and consequently the total pressure of the steam
in the cylinder, is 50 lbs. per square inch, is it not
true, that provided the steam be abundantly fur-
nished at that pressure by the heating surfece, it is
quite indifferent whether till the moment of being
used, it has been stored in the boiler under a
pressure of 65, or 75, or 95 lbs. per square inch ?
That steam must always, definitively, at the moment
of action, be transformed into steam at only 50 flbs.
of pressure ; and the velocity will depend solely on
the quantity of steam at the pressure of 50 lbs.,
which shall have been furnished by the boiler. It
is very erroneously then that engine-men are fre-
quently seen to augment the pressure in the boiler
of the engines, in the hope of obtaining a greater
velocity. It is the vaporization, and not the pres-
sure, that must be augmented, and it is very
OF THE BFFBCTS OF THE ENGINES. 343
probable that if the truth, in this respect, were more
generally known, steam engines, and particularly
those of steam vessels, would be liable to fewer
explosions ; for a great number of those accidents
are to be attributed to the desire of obtaining a
greater velocity, which the engine-man flatters him-
self of being aUe to attain by augmenting consider-
ably the pressure in the boiler, by means of the
safety-valves.
With regard to the quantities contained in the
formulae, we have indicated above the manner in
which each of them ought to be expressed, and it
will have been remarked that we have referred all
the measures to uniform unities, namely : the foot,
the pound, and the hour, as respective unities of
length, weight, and time. The observation of this
rule is absolutely indispensable, in order that the
formulae may be what is called homogeneous^ and con-
sequently that they give an exact result. This is
a remark on which we deem it necessary to insist,
because, in practice, some of the quantities which
we employ are expressed in inches, others in pounds
per square inch, or sometimes in atmospheres, &c.,
according as it may seem most commodious for
common use ; and if all these measures were not
restored to homogeneity, none but a most erroneous
result could be obtained.
In order however that no difficulty may occur on
this head, we shall, in the sequel, resume this
subject, in transforming the obtained formulae into
344 CHAPTER XII.
practical formulae, and shall then give an example
of the application of each of them.
Lastly^ before passing to another, problem, we
most yet remark that the formula which we have
obtained above, differs in appearance from that
which we have given for the same purpose, in the
work entitled Tlieory of the Steam Engine. But the
reason is merely that some of the terms in it are
more developed, and, besides, that the velocity
here calculated is that of the engine and not of the
piston, which has obl^ed us to refer the different
resistances, not to the velocity of the piston, as in
the work just cited, but to the vekxuty of the engine
expressed in miles per hour.
Sect. V. Of the load of the engine for a desired
velocity.
The object of the preceding research was to
determine the velocity of the engine for a fixed
load. But if, on the contrary, the velocity be given,
and that it be desired to know what load the engine
can draw at that velocity, on a plane of a deter-
mined inclination, then it will suffice to resolve the
equation (1 bis) with reference to M, and we shall
have for the value of M,
This equation then will make known the load, in
OF THE EFFECTS OF THE ENGINES. 345
tons gross, tender included, which corresponds to
the velocity v.
It is necessary, however, here to observe that there
are many ways of expressing the load of the engines
in practice. It is most commonly expressed as we
have done it, in tons gross, tender included, that is,
including the weight of the tender of the engine.
But, for certam inquiries, it is more convenient to
express it, either in tons gross, tender not included ;
or in elective tons of goods, that is, exclusive both
of the tender and of the waggons. To pass from
the first of these expressions to the two others, we
have evidently but to subtract the weight of the
tender in the first case, and the weight of both
tender and waggons in the second.
Thus, expressing by C the weight of the tender,
the load of the engine, tender not included, will be
M-C;
and expressing by - the average ratio of the weight
of the goods carried on a waggon, to the total
weight of the loaded waggon,
i(M-C)
t
will be the load of the engine in effective tons.
On railways of not more than about 5 feet of
breadth of way, and for an engine weighing from 8
to 12 tons, the average weight of the tender may be
valued at 6 tons, and the efiective load of the wag-
346 CHAPTER XII.
gons is commonly f of their total weight. We have
then for the different expressions of the load,
M, load in tons gross, tender included ;
M— 6, lottd in tons gross, tender not incladed ;
•|M->4, load in effective tons.
It must be observed that the formula which we
have just obtained, contains in its second member
the term wt;*, in which u depends on the number of
carriages in the train, as has been seen, Chapter IV.
The precise value of this term could not then be
determined till after the load of the engine be
known, which is the quaesitum of the problem ; but
recourse will be had to approximations, as in the
preceding research : that is to say, the second mem-
ber of the formula must be calculated, exclusively of
the term in which the quantity u figures, and calling
B the result of that calculation, we have
Ic±g
Then making a first valuation of the quantity w, and
substituting it in the equation, we shall conclude a
corresponding value of the load M. If that load be
such as to require for u the value supposed, or very
nearly so, it is the load sought, and the problem
is solved. But if the load thus found show that the
value supposed for u was erroneous, it must be used
to make a new valuation of u more exact than the
first: this will consequently lead to a new deter-
mination of M, which will likewise be more approx-
OF THE EFFECTS OF THE ENGINES. 347
imate than the fonner; and were it necessary, a
third approximation might be made. But in general
two trials will suffice ; be it as it may, the equation
is so simple, that these essays will be made rapidly
and without the least difficulty.
Examining the formula which we have obtained
above for the load of the engine, it will be remiarked
that taking the cases wherein g is preceded by the
sign minuSy and making k—g^=^Oy that is, supposing
the motion to take place in descending an inclined
plane on which the friction of the waggons is
counterbalanced by their gravity, the formida seems
to give, for the suitable solution of the problem,
M=i.
0
But this apparent result depends only on the cir-
cumstance that un^ is not developed, and that it is
really a function of M. In effect, we have seen,
Chapter IV., that the value of wv', which represents
the resistance of the air, depends not only on the
transverse section of the train, but likewise on the
number of carriages which compose it, and conse-
quently on the weight of the train. The result
obtained above is then caused simply by the co-
efficient of the only term in which the quantity M
is expressed, becoming null by the supposition of
ft — 9=0 ; but it will presently appear that referring
to the value of the term wi;*, the weight, of the load
M is no less limited and easy to determine.
348 CHAPTER XII.
In effect, if we resume the equation (2) and write
it under the form
(*±ir)M±^ + «r3=-i-rJ^. ' ?.- F- ^ll+p + p'v)],
l + aL5280 /+e 90 D\q ^ fj
it will be recognised that the first member expresses
the total resistance opposed by the train, namely,
the gravity and friction of the waggons, the gravity
of the engine, and finally, the resistance of the air
against the train. But if, in this equation, we make
k—g=^Oy it becomes
that is to say, in this case, the resistance of the train
reduces itself to that of the air diminished by the
gravity of the engine. The quantity M then osten-
sibly disappears firom the equation, but it neverthe-
less remains represented by the term uv^y and by
this term will be obtained the solution sought ; for
resolving the equation with reference to wt;^, we
derive
--n:.tii,-,4-4-'-*'(r*'*'--)]*'-
Now the velocity of the motion is given. There-
fore this equation will make known the quantity u ,
and, as a consequence, the effective surface offered to
the shock of the air by the train in motion. But
we have seen. Chapter IV., that, for a railway of 5
feet of width of way, that efiective surface is equal
to 70 square feet, plus as many times 10 feet as
there are waggons. We may then, from the know-
OF THB EFFECTS OF THE ENGINES. 349
ledge of II, deduce the number of carriages/ and as
we know besides the average weight of a carriage,
we shall conclude, in fine, the definitive weight of
the train, which will be limited and not infinite.
There is yet another case in which the formula
just obtained for the load of the engine, seems to
give the result of M= - : it is the case wherein
0
it is supposed t; = o. The consequence then would
be that the load corresponding to a velocity null
would be infinite. But observing the formula more
attentively, we recognise that it by no means gives
this result. It will be recollected, in effect, that
the quantity S represents the effective vaporization
of the engine, or the volume of water which really
passes, in the state of steam, into the cylinders.
Now if we suppose the velocity null, it is evident
that no steam at all can pass into the cylinders,
since that steam could not traverse them without
driving the pistons, and consequently creating some
velocity in the engine. The supposition therefore
of r = 0 necessarily carries with it that of S = o,
and consequently the value of M then presents itself
under the form
0
Thus, in this case, the formula reduces itself to the
indeterminate form; but it must be observed that
the formulae under consideration are intended to
350 CHAPTER XII.
make known the effects of the engine, only when
it has attained unifonn and permanent motion.
Now it will presently be seen, in seeking the velo-
city of maximum useful effect, that for a given
vaporization S, the uniform velocity of the engine
can never be less than
._ 1 S JD^ 1
^ ~5280' d«' l+c n+jP'
because this velocity is that which corresponds to the
passage of the steam into the cylinders in its state of
greatest density or highest pressure, and that at any
other less density, the steam would necessarily oc-
cupy a greater volume, and consequently could not
traverse the cylinders without producing a greater
velocity in the engine. All supposition of a smaller
velocity than the above is therefore inadmissible in
the problem, as being incompatible with the state of
permanence and uniformity of motion for which
alone the effects of the engines are calculated.
Sect. VI. Of the different expressions of the useful
effect of the engine.
We have said that there are many modes of
expressing the useful effect of the engines. We
are about to consider each of them successively.
1st. The useful effect produced by an engine in a
given time, is the product of the mass conveyed
and the distance to which it is conveyed, in the
OF THE EFFECTS OF THE ENGINES. 351
given time. Now, in the engines under considera-
tion, the mass conveyed is represented by the
quantity M, or by the number of tons drawn by
the engine. The velocity t; likewise expresses the
distance traversed by the engine, or, in other words,
the distance traversed by the load, during the unit
of time. Hence the product M i; is no other than
the useful effect produced by the engine during the
unit of time.
To obtain the expression of this useful effect, it
wiU consequently suffice, to draw from equation (2)
the value of M t;, which will be done by multiplying
both terms by v ; and thus we shall have
(l + 8)(*+^) L5280 i+e q V \q / J *±^
We have thus the solution of the problem ; and it
will be observed that this expression of the useful
effect, for a given vaporization S, varies with the
velocity of the engine, as may have been already
remarked in the experiments which we have pre-
sented, Sect. II. Chapter XL
In practice, the desired result may be attained
more simply, by seeking first, from equation (2),
the numerical value of the load M corresponding
to the velocity t;, then multiplying that load by the
given velocity. For instance, we have already
found. Sect. iv. Article I. of this chapter, that at
the velocity of 19'67 miles per hour, and ascending
a plane inclined j^, an engine of the dimensions
352 CHAFTEE Xll.
before indicated, would draw a kiad erf* 50 tons.
We are then to condnde that the nsefbl dEkdt
which the esu^ne will prodace at that velocity and
on that plane, will be 983 tons omveyed 1 mile per
hour.
Hie solution whidi we have just given oi the
problem suits the case in which it is required to
find the useful effect produced at a kno¥m velocity.
But if, on the contrary, the load is given, and it be
required to find the useful effect that the engine
will produce with that load, then the velocity
corresponding to the ^ven load must first be
sought, finom equation (1) or (1 bis), and that
velocity multiplied by the given load will be the
corresponding useful effect.
We must here call to mind that the load M of
the engine is measured in tons gross, tender in-
cluded, and consequently the useful effect Mv is
the useful effect of the engine in tons gross dra?m
1 mile, tender included. But as we have seen that
representing by C the weight of the tender, and by
-r the ratio of the effective load of a waggon to its
total weight, the load of the engine may be ex-
pressed m tiuee ways, namely:
M, . . • . load in toDB gross, tender incloded ;
M— C» . . load in tons groas, tender not included ;
-r (M^C)» load in effective tons ;
t
it is plain that the useful effect of the engine, in
OF THE EFFECTS OF THE ENGINES. 353
tons drawn 1 mile, may be likewise expressed in
three ways, which are :
Mv, .... useful effect, in tons gross drawn I mile, tender
included ;
Mv— Cv, . useful effect, in tons gross drawn 1 mile, tender
not included ;
-- (M^C) V, useful effect, in effective tons drawn 1 mile.
t
We have already said that on railroads of but
about 5 feet of width of way, the average weight
of the tender may be valued at 6 tons, and the
effective load at f of the gross load ; we have there-
fore C = 6 and ^ =f . Thus in the example above
mentioned, the useful effect of the engine, in tons
gross drawn 1 mile per hour, may be expressed in
the three following manners :
983 tons gross drawn 1 mile, tender included ;
865 tons gross drawn 1 mile, tender not included ;
577 effective tons drawn 1 mile.
The three modes which we have just indicated to
express the load, and consequently the useful effect
of the engines, are all in use ; the choice among
them depends merely on the object in view at the
time. As, however, they may easily be concluded
one from another, and as the most simple consists
in taking the load, in tons gross, tender included,
this will be the method which we shall employ.
The only exception which we shall make to this
2 a
354 CHAPTER XII.
rule, will be in the inquiry as to the expenditure of
coke and water per ton per mile, in which, to con-
form to the usual practice, we shall refer the ex-
penditure to the load, in tons gross, tender not
included. But, in every other case, we will suppose
the load and the useful effect measured in tons
gross, tender included, and it will always be this
that we intend to signify by the usejul effect of the
engine, when we do not specify to the contrary.
2nd. The expression furnished by formula (3), or
the equivalent mode of calculation which we have
pointed out, makes known the useful effect of the
engine, in tons conveyed 1 mile in tm hour. But,
as we have before said, the useful effect of an engine
may be expressed under several forms. It will be
proper then to seek those different expressions.
A very simple mode of making known the effect
of an engine, consists in representing it by the
number of horses that would be required to produce
the same effect, not at the same velocity, but in the
same time. With this view, the expression one
horse-power has been made to designate an efiect
of 33000 ftsr raised one foot per minute. This
measure has arisen from the observation having
been made that a vigorous horse going at a walking
pace, or about 220 feet per minute, which is the
most advantageous speed, may, permanently and
without fatigue, exert an effort of 150fts., or, in
other words, raise a weight of 150fts. suspended
at the end of a cord which passes over a pulley.
OF THE EFFECTS OF THE ENGINES. 355
It is plain that, in this labour, the useful effect
produced is 33000 fi>s. raised 1 foot per minute,
and it is for this reason that this effect is designated
by the name of horse-pawer; but it would be much
more exact, as we have remarked in another work,
to call it horse-effect^ since it is an effect and not a
force. It would then be said that an engine is of
so many horse-effect, instead of saying that it is
of so many horse-power. The expression would
be more correct; but it suffices to have a clear
understanding as to the value of the terms.
To apply the measure which has just been given,
to the effect of locomotive engines, it suffices to
observe that the traction of one ton gross, on a rail-
way, offers a resistance of 6 lbs., that a mile repre-
sents a length of 5280 feet, and that an hour con-
tains 60 minutes. Any useful effect then whatever,
expressed in pounds raised 1 foot per minute, may
be transformed into tons gross drawn 1 mile per
hour, by multiplying by the factor,
60 _ 1
6 X 5280 ~ 528 '
and consequently the force or the effect of one
horse, expressed in this manner, is represented by
33000
^ = 62*5 tons gross drawn 1 mile per hour.
As soon as the effect of one horse has thus been
referred to the usual measures on railroads, nothing
356 CHAPTER XII.
is more easy than to find the effect of a locomotive
engine, in horse-power. For that purpose, it evi-
dently suffices to divide the useful effect Mv already
obtained, by the new unity adopted. We have
thus the number of those unities which represent
the effect M r, and consequently the useful eflfect of
the engine expressed in horses. Tliis effect then
will be
U.E. inHP.= ^.
625
It will be remarked that the product M v, or the
useful effect of the engine, varies with the velocity
of the motion ; and it will be seen further on that
this product is by so much greater as the velocity is
less.
It is the same with effects produced by horses ;
for we know that the useful effect due to their
labour decreases rapidly as their speed increases,
and that it is only at the most advantageous speed
that this effect can be valued at 33000 lbs. raised
1 foot per minute. When therefore the useful
effect of an engine is expressed, under whatever
form, it will always be necessary, in order to be
exact, to relate at the same time the velocity at
which that effect is produced, or, which amounts
to the same, the load with which it is produced;
and if this measure is used in an absolute manner,
as it is with respect to the horse, it should then be
understood that the effect indicated is that of the
OF THE EFFECTS OF THE ENGINES. 357
most advantageous labour of the engine. As we
shall presently obtain the measure of the maximum
useful effect a given locomotive engine can produce,
we may then also express that useful effect in horse-
power. It will be this valuation then, that is to
say, the greatest effect the engine can produce,
working at the minimum or most advantageous
velocity, that we shall always intend, when we say
in an absolute manner that an engine is of the effect
or of the force of so many horses ; but, in every
other case, in indicating the effect of an engine in
horse-power, we shall always express at what velo-
city or with what load such effect is produced.
3rd. In the two preceding questions we have ex-
pressed the total effect the engine can produce in
the unit of time, without regard to its consumption
of water and fiiel. We are now going, on the con-
trary, to express that effect with reference to the
expense which is necessary to produce it.
The useful effect obtained in equation (3) , is that
which is produced by the effective vaporization S of
the engine, or, in other words, by the total vaporiza-
tion S' of the boiler ; and as we have seen that this
vaporization S or S' is that which takes place in the
unit of time, the corresponding useful effect is also
the useful effect produced during the unit of time.
But if it be supposed that to effect this vaporization
the engine requires the consumption of Nibs, of
fuel, it is clear that then N lbs. of fuel will be suf-
ficient to draw 1 mile a number of tons expressed
358 CHAPTER XII.
by Mv. Therefore, by a simple proportion, the
quantity of fuel necessary to draw a ton 1 mile
will be
N
Mi;
It will, however, be observed that the quantity M
indicates the load of the engine, tender included.
The number Mv represents then the number of
tons, tender included, the conveyance of which 1
mile has been performed by the weight N of coke ;
and consequently the • result which we have just
obtained expresses the weight of coke expended
per ton gross per mile, tender included, that is,
taking into the calculation the weight of the tender.
But if it be desired, as is customary on railways,
to know the expenditure of fiiel which will be neces-
sary for a given work, tender not included^ recourse
must then be had to the expression of the useful
effect of the engine, in tons 1 mile, tender not
included. We have seen that expressing by C the
weight of the tender, the useful effect of the engine
expressed in tons gross conveyed 1 mile, tender not
included, is
(M-C)i; = Mt;-Ct;.
Since, therefore, this effect is produced by the con-
sumption of N lbs. of coke, the quantity of coke, in
pounds, necessary, per ton gross per mile, tender not
included, will be expressed by
OF THE EFFECTS OF THE ENGINES. 359
N
Q. CO. pr. t. pr. m. =
Mr-Ct;
To apply this formula it will suffice to know the
number of pounds of coke consumed in the fire-box,
to operate in the boiler the total vaporization S' ;
which the experiments developed Chapter XI. have
enabled us to do. It will therefore be easy to solve
the problem proposed.
It is yet to be observed that the quantity of coke
necessary per ton per mile, must vary in the same
engine, with the velocity of the motion; because
the product M t; is by so much the smaller as the
velocity is greater, whereas we have shown, in
treating of the fuel, that the quantity N, or the
expenditure of coke necessary to operate a deter-
mined vaporization, varies but in an insensible de-
gree with the velocity. This result as to the vari-
ation of fuel per ton per mile has already been
noticed, Chapter XI.
4th. From what we have said above, the effective
vaporization S has sufficed to draw 1 mile a number
of tons gross expressed by M v, tender included, or
by (M— C) Vy tender not included. The quantity
therefore of water effectively vaporized, which has
performed the conveyance of a ton 1 mile, tender
hot included, is expressed by
S
Mv — Cv
But as it is more convenient to refer the useful
360 CHAPTER XII.
effect to the total or gross vaporization of the
boiler, and as we have expressed this by S', we
shall have for the quantity of total vaporization,
necessary to draw 1 ton gross 1 mile, tender not
included,
Q. wa. pr. t. pr. m. =
Mv-Cv
5th. To obtain the useful effect produced per
pound of fuel, it is to be observed that, since the
useful effect M v has been produced by the consump-
tion of N lbs. of coke, the useful effect produced by
each pound of coke must be the Nth part of the
above effect. Thus this useful effect, expressed in
tons gross drawn 1 mile, tender included, will be
U. E. lib. CO. = -=r=-
N
6th. Similarly, to obtain the useful effect pro-
duced per cubic foot of water vaporized, it will be
observed that, since the useful effect Mt; is that
which is due to the total vaporization S' of the
boiler, that is to say, to the number S^ of cubic feet
of water vaporized, the useful effect produced by
the vaporization of 1 cubic foot of water will be
had by dividing the useful effect M t; by the number
of unities that there are in S\
Thus the useful effect produced per cubic foot of
total or gross vaporization, and expressed in tons
gross drawn 1 mile, tender included, will be ex-
pressed by
OF THE EFFECTS OF THE ENGINES. 361
Mv
u. E. 1 ft. wa. =
S'
7th. We have obtained, in the 5th problem, the
useful effect produced per pound of fuel. It will
therefore be easy to deduce the number of pounds
of fuel necessary to produce the effect of one horse.
*
A simple proportion will evidently suffice, and the
quantity of fuel, in pounds, which produces the
effect of one horse, will be expressed by
62-5 N
Q. CO. pr. HP. =
Mv
8th. We find in the same manner, by a simple
proportion, the quantity, in cubic feet, of total
water vaporized, which produces the effect of one
horse, namely :
r\ xjD 62-5 S'
Q. wa. pr. HP. = — .—
Mv
9th. The effect, in horse-power, produced by the
consumption of 1 ft. of fuel, will evidently be
Mv
u. E. in HP. of 1 ft. CO. =
62-5 N
And, 10th, finally, the effect, in horse-power, pro-
duced per cubic foot of total water vaporized, will
be expressed by
u. E. in HP. of 1 ft. wa. = ^^^.
625 S
362 CHAPTEE XII.
ARTICLE 11.
OP THE MAXIKUlf U8BFUI« EFFECT OF THE ENGINE.
Sect. I. Of the velocity of maximum useful effect.
We have hitherto detennined the effects of the
engines in a maimer perfectly general, that is to
say, taking the data of the prohlem without re-
stricting them to any condition, except only that
of being contained within the limits of the power of
the engine. But an important question now pre-
sents itself. It is proposed, among all the different
velocities that can be imagined for the engine, and
each necessarily implying a certain corresponding
load, to determine that which will produce the
greatest useful effect. This problem is of great
utility, since it shows in what case the engine will
work in the most advantageous maimer possible.
To solve this question, we must recur to the
general expression of the useful effect produced by
the engine, and seek what value of v will make it a
maximum. This general expression is given by equa-
tion (3) , namely :
Now, in observing this expression, we find that
the velocity figures only in the negative terms ; for
OP THE MAXIMUM USEFUL EFFECT. 363
the factor ; could become negative, that is, change
the apparent sign of the other terms, only in the
case wherein the motion should be descending, and
wherein at the same time we should have g>k.
But in that case the train would be found placed on
an inclined plane on which the waggons would roll
of themselves; and consequently the useful effect
Mv would no longer be the result of the force
of the engine alone, but of that force joined to the
gravity^ which would become an effective motive
force. To know therefore the conditions which
render the useful effect of the engine a maximum,
this case must be excluded ; and thus we see that,
in the expression brought forward, so long at least
as it expresses only the effect proper to the engine,
the velocity figures only in the negative terms.
Hence, firstly, the greatest useful effect will take
place at the lowest value of v.
But, from equation (1), the velocity v is ex-
pressed by
1 iiS D
V =
5280 d^ l + c'
and it is clear that, for given dimensions and vapor-
ization, this expression will be at its lowest value,
when fi is the smallest possible. On the other
hand, as the quantity fi represents the volume of
the steam under the pressure R, it will evidently be
at its least value when the pressure, or resistance R
364 CHAFTEE XII.
against the piston, shall, on the contrary, be at its
maximum. Hence, finally, the maximnm useful
effect of the engine takes place when the load is
the greatest possible.
Now, it is plain that, the resistance R can in no
case exceed the pressure of the steam in the boiler,
since the resistance would then be greater than the
motive power, and the motion would thus become
impossible. The maximum therefore of R, the
minimum of r, and the maximum possible useful
effect of the engine, will be given by the conditional
equation
R=P.
Consequentiy, if we express by ik the relative
volume of the steam generated under the pressure
P of the boiler, the velocity of maximum useful
effect will be determined by putting ii! instead of
Ik in equation (1) ; that is to say, that velocity
will be
1 /S D ,.,
5280 d« l^c ^ ^
or else, by putting for lu its value,
.^ 1
^ ~n+}P'
that velocity may again be expressed by the formula
- 1 S D 1 , - , . ,
V = ^^^^- -- • -; • =r- .... (4 bis)
5280 e? /+c n+^P ^ ^
This equation then will make known the velocity
corresponding to the maximum useful effect of the
OF THE MAXIMUM USEFUL EFFECT. 365
engine, as soon as the quantities S, d, D, / and P
shall be replaoed by their value taken on the engine,
and referred to homogeneous measures, as has been
already said.
Sect. II. Of the load corresponding to the maximum
of useful effect.
The load corresponding to the maximum of useful
effect will be known by equation (2) , on substituting
in it instead of v, the value v' given above. But it
will be obtained more simply, by deducing it di-
rectly from the condition
R=P,
which, substituting for R its value (Chapter IX.),
becomes
(1 + 8) [(*±^)M tgm + iii;»] -?^ + ^ +/> + A=P,
and which, when v is replaced by v\ gives
^'-(TH|b5(^-'-'''^-iF/-ni ±'")-:S ^*>
This formula, in which account must be taken of
the variation of the term wv'^, as has been said,
Sect. V. of the preceding article of the present chap-
ter, will make known the load that ought to be given
to an engine to make it produce its maximum useful
effect.
It is necessary here to remark, that as this load
offers a resistance precisely equal to the pressure of
366 CHAPTER XII.
the steam in the boiler, and as we have seen that at
the moment of starting of every engyie, the power
must necessarily exert an effort greater than the
resistance, it would be impossible for the engine
to set itself in motion with the load M'. If then
we would make the engine work with this load,
it is understood that the aid of another engine
would be requisite to start it ; or else the engine-
man must for a few minutes close the safety-valve,
to create in the boiler a sufficient excess of pressure,
till the uniform motion be attained. Then the mo-
mentary excess of pressure may be withdrawn, and
the engine will continue its motion without any
external aid.
However, as on railways there continually occur
little inequalities or accidental imperfections in the
road, and as the engine ought to be capable of over-
coming them, it is not to be expected that it can
be made to perform an entire trip, working pre-
cisely at its maximum of useful effect, or with its
maximum load. The preceding determination there-
fore is to be considered only as showing what the
engine may perform on arriving with a velocity
already acquired, at an inclined plane situated at
a certain point of the line, or as indicating the
point towards which our aim should tend as much
as possible, in order to accomplish producing the
maximum of useful effect, but without reckoning on
obtaining it completely in practice.
We here neglect the little necessary difference
OF THE MAXIMUM USEFUL EFFECT. 3C7
between the pressures in the cylinder and in the
boiler, from the flowing of the steam from the one
vessel to the other. It plainly tends somewhat to
reduce the load of the engine, increasing in a cor-
responding manner the velocity of maximum useful
effect.
Sect. III. Of the measure of the mcurimum useful
effect of the engine.
The maximum usefiil effect of the engine will
evidently be the product M'v\ Consequently,
after having determined the velocity and the load,
as has just been explained in the two preceding
sections, it will suffice to multiply together the two
quantities obtained. Thus we shall have
m. u. E. = M'i;' (6)
The developed expression of the maximum useful
effect might be obtained immediately, by performing
the multiplication of the two values of v' and M'
given by the equation^ (4 bis) and (5) ; but as it
is much more simple to solve these two equations
separately to derive v' and M' from them first, and
then to multiply the two results together, as has
just been pointed out, we will follow this mode of
calculation.
To obtain the effect of the engine in horse-power,
when working at its maximum of useful effect, and
in like manner to obtain all the other modes of
368 CHAPTER XII.
expressing the effect produced, it evidently will
suffice to substitute, in the general formulae given
on this head in the preceding article, for the pro-
duct Mr, the product M'l?', which is suitable to
the production of the maximum useful effect. We
shall not dwell here on the divers expressions, since
they would be but the reproduction of the formulae
already explained.
ARTICLE III.
PRACTICAL FORMULiE FOR CALCULATING THE EFFECTS
OF LOCOMOTIVE ENGINES^ AND EXAMPLES OF THEIR
APPLICATION.
We have hitherto presented the formulae proper
for calculating the effects of the engines, under a
form completely algebraical, that is to say, leaving in
them all the quantities represented by letters, with-
out excepting the constant quantities whose values
have been already determined in former chapters.
But we now purpose to reduce these formulae to
their most simple practical form ; in order to effect
which, it will be proper to replace in them, as far as
may be, the letters by the numerical values which
they represent.
'The letters which have a constant value in all
cases and for all the engines are :
ky Friction of the waggons, which we have found
equal to 6 lbs. per ton ;
PRACTICAL FORMULiE. 369
jp, Atmospheric pressure, the. value of which is
21 18 lbs. per square foot;
n, Constant quantity relative to the volume of the
steam, its value being '0001421, when the
pressure is measured in pounds per square
foot;
9, Factor relative to the volume of the steam, equal
to .00000023 when the pressure is expressed
in poundfl per square foot ;
c. Clearance of the cylinder, which may be taken
generally at ^ of the useful stroke of the pis-
ton, which gives -— — = — -.
^ l + c 21
These values being constant for all engines, may
be introduced permanently into the equations. Sub-
stituting them therefore for the respective letters,
and effecting the calculation as much as possible,
we obtain the following formulae, which are quite
prepared for practical applications.
In order to avoid recurring to another page of
the work, we will first repeat here the signification
of all the letters which subsist in these formulae.
M, Load of the engine, in tons gross, tender in-
cluded ;
m. Weight of the engine, in tons ;
C, Weight of the tender, in tons ;
gy Gravity, in poimds, of 1 ton placed on the in-
clined plane to be traversed by the engine.
2b
370 CHAPTER XII.
If the inclinatioii of the plane be -, that gra-
vity will have for its value, in pounds, ;
and if the plane be horizontal, the gravity
will be equal to zero ;
17, Velocity of the engine, expressed in miles per
hour;
vr^. Resistance of the air against the train, at the
velocity 17, a resistance expressed in pounds ;
p^v. Pressure owing to the blast-pipe, expressed in
pounds per square foot ;
F, Friction of the engine, in pounds ;
S, Additional friction of the en^e, measured as
a fraction of the resistance, namely : '14 for
engines with imcoupled wheels, and *22 for
those with coupled wheels ;
D, Ditoieter of the propelling wheels, in feet ;
dy Diameter of the cylinder, in feet ;
2, Stroke of the piston, in feet ;
P, Total or absolute pressure of the steam in the
boiler, in poimds per square foot ;
S, Effective vaporization of the engine, in cubic
feet of water per hour. It varies according
to the engines, but may, on an average, be
valued at *75 of the total or gross vaporiza-
tion, when there is no blowing of steam at
the valves ;
S^ Total vaporization of the boiler, at the velocity
PRACTICAL FORMULiE. 371
of the motion, in cubic feet of water pei:.
hour;
N, Consumption of coke in the fire-box, in pounds
per hour.
PRACTICAL FORMULA FOR CALCULATING THE EFFECTS
OF LOCOMOTIVE ENGINES.
General case.
f»»* -rr, • • • • Velocity of the en-
(1 + Z) [(6±y)M ±^ + iiii»] + P + ^(2736 +y») gine, in miles per
hour.
Load of the engine,
in tons gross, tender
included.
0. E s M 9 Useful effect, in
tons gross drawn
1 mile per hour,
tender included.
u.B.inHP ""Hx U"^ «®«^' "^
horse-power.
Q. CO. pr. t. pr.m... »— - — — - Quantity of coke
m pounds, per ton
gross drawn 1 mile,
tender not included.
S'
Q. wa. pr. t. pr. m.. . «— —_ Quantity of water,
in cubic feet, per
ton gross drawn 1
mile, tender not in-
cluded.
u.E.llb.co. =.-— Useful effect pro-
duced per pound of
coke, in tons gross
drawn 1 mile, ten-
der included.
372 CHAPTER XII.
iLB.lft.wa. ....=^^ Uiefid eflfect pro-
duced per cubic foot
of tottl T^orizft-
tioDt in toDi groM
drawn 1 mile, ten-
der included.
Q.co.fr. 1 HP.....=5^|-^ Quantity of coke in
pounds, which pro-
duces the eflfect of
1 horse.
Q.wa.fr.lHP.....-5?^A Quantity of water,
in cubic feet, which
produces the effect
of 1 hone.
U.B. llb.co.inHP.--g^l^ Useful effect, m
horse-power, pro-
duced per pound of
o^e.
u.E.lft.wa.inHP.»g|L!L. Useful eflbet, in
hofse-power, pro-
duced per cubic
foot of totai ^vpOT'
isation.
Case of maximum tisejvl effect,
^-^^ D s
1-421 + -0023P7'S velocity of man-
mum useful effect,
in miles per hour.
Maximum load of
the engine, in tons
gross, tender in-
cluded.
itLU.E. «M'9' Maximum nsefol
effect, in tons gross
drawn 1 mile per
hour, tended in-
cluded.
PRACTICAL formula:. 373
We do not give the divers modes of expressing
the maximum of useful effect in horse-power, &c.y
because those formulae are the same as in the
general case, on merely replacing M and v by M'
and v\
That there may be no misunderstanding as to the
manner of expressing the divers quantities contained
in the formulae, nor on the manner of performing
the calculation, we will here give an example or
two with some detail.
Suppose then a locomotive of 65 cubic feet of
total vaporization, at the velocity of 20 miles per
hour; with cylinders 11 inches or *917 foot in
diameter, stroke of the piston 16 inches or 1*33
foot, wheels 5 feet in diameter, not coupled, friction
103 fts., weight 8 tons, blast-pipe 2*33 inches in
diameter, total or absolute pressure in the boiler
65 fi>s. per square inch, and consumption of coke
per hour 598fi>s. Suppose this engine employed
on a level railway, of about 5 feet of width of way,
and let it be required to know what velocity it will
attain with a train of 10 waggons weighing 56 tons,
tender included, which is the same aa 50 tons with-
out tender.
1st. As the motion takes place on a horizontal
plane, we have ^ = 0 ; and since the wheels of the
engine are not coupled, we have S = -14 = ^.
Moreover, from the ratio which we have found
between the total and the effective vaporization
374 CHAPTER XII.
of the engine, the value of the latter, at 20 miles
per hour, is
S = '75 X 65 = 48-75 cubic feet of water per hour ;
and in fine, from the proportions of the engine,
we have
^ ="w' X ^ = -2237.
This done, to find what velocity the engine
will acquire in drawing the train of 56 tons, we
will first suppose that it may be, approximatively,
23 miles per hour, and we shall then have, for the
pressure in the blast-pipe, 4 Hbs. per square inch, or
p'v = 576 lbs. per square foot. As the efibctive
surface presented to the shock of the air, valued
according to the mode explained Chapter IV., is
5'=70 + 10X 12=1 90 square feet, the resistance
of the air at the velocity of 23 miles per hour, will
be uv^ = 270.
Thus the value of v, taken without supposing
that the vaporization changes with the velocity,
will be
^ 784x48-75
^"^ 114 (6x56 + 270) +103+2237 (2736 + 576) "•^^*^^"'
This first essay of calculation gives then 24*88
miles per hour, for the velocity of the engine,
and we conclude from it that the two terms uv^
and p'v which we have calculated on the supposi-
PRACTICAL FORMULA. 375
tion of t7 = 23, have not been valued in a manner
sufficiently exact, but that the true velocity is com-
prised between 24*88 and 23 miles.
Trial then might be made of t; = 24, and this
value would be found to satisfy the problem, when
the variation which the vaporization undergoes with
the velocity of the motion is neglected. Thus ap-
proximatively we might hold to this result ; but if
it be desired to calculate with greater accuracy, it
will be proper to introduce the increase of vaporiza-
tion due to the velocity.
For this purpose, as the increase of vaporization
will have the effect of increasing the result of the
calculation, we will try a number greater than 24,
as v = 25, for instance. Supposing then this datum
for the valuation of the variable quantities, we shall
have
S = 51-55,
pv = 630,
wt;^ = 319;
and resolving the equation with these values we find
i; = 2519.
Consequently, in fine, taking a mean between 25
and 25*19, we have, for the definitive velocity
sought,
V = 25*10 miles per hour.
Such then wiU be the velocity which the engine
will assume, when drawing on a level a train of
56 tons, tender included.-
376 CHAPTER XII.
2nd. To continue this example of the application
of the formulae, let it he required to find what will
be the velocity of the maximum useful effect of the
engine.
In order to effect this, we will replace in the
equation proper to that problem, the pressure P
in the boiler by its value P= 65 X 144=9360*6.
per square foot ; and supposing first that the vapor-
ization of the engine will undergo no change not-
withstanding the reduction of velocity, we obtain
the result
,,> _ 1-804 X 48-75 1 ,.,«
^ - 1-421 -h 0023 X 9360 ':2287=^^^^-
This would then be the velocity sought, if the vapor-
ization of the engine were invariable ; but as the
diminution of velocity will lower the vaporization,
which is such as we have supposed it, only at the
velocity of 20 miles per hour, we will try whether
the velocity of 16 miles will suit the formula.
Then the effective vaporization of the engine, re-
duced in the proportion of the fourth roots of the
velocities, will become 46' 10 cubic feet of water
per hour, and the formula resolved according to
this supposition, will give
v' = 16*20 miles per hour.
This is therefore the velocity suitable to the pro-
duction of the maximum useful effect required.
3rd. In fine, to obtain the load corresponding to
the maximum of useful effect, we recur to the proper
equation, which is
I
I
I
I
!
I
I
I
I
PRACTICAL FORMULA. ' 377
^ =-5-60+1) ^^-^^*^-^*^-6(T+F)"-6- '
and first calculating in this all the termSi except the
last, we have as a result
208-46.
It remains then to subtract from this number
•Iff *
the value of -^-» to conclude from it definitively
the required value of the load. As the value of
the term
depends on the number of carriages in the train,
which will itself be known only by the definitive
solution of the problem, we wiU again in this place
follow the method of approximations. Supposing
the load to be of about 160 tons, the train will
consist of 31 carriages besides the tender; thus
the efiective surface offered to the shock of the
air, will be
X = 70 + 33 X 10 = 400 square feet.
Consequently the resistance of the air, at the velocity
found, of 1 6'20 miles per hour, will be uv' ^=282 lbs.,
which gives
^=4700;
substituting then this valuation in the formula, we
obtain the result
378 CHAPTER XII. •
M' = 208-46 ^ 4700 = 161-46.
Consequently the load of 161*5 tons, forming a
train of 31 carriages, besides the tender, will be
the maximum load required.
4th. In fine, if it be desired to know the maxi-
mum velocity the engine is capable of attaining,
when followed by its tender only, and without
drawing any train, the proceeding will be as in
the first case; but supposing the load to be of
6 tons only, and taking account of the increase
of vaporization, according to the velocity, the re-
sult will be
r = 35*03 miles per hour.
In this last case, the useful efiect of the engine,
tender not included^ will be null.
From these detailed examples is seen how the
calculation is to be performed in all the cases;
but it must be remarked, that with the use of
logarithms, these different trials present no sort
of difficulty, and that those who have once got
the habit of these researches, guess immediately
and at a glance, what numbers they ought to
employ in the approximations, so that the apparent
length of the calculation entirely disappears.
Collecting the results which we have just ob-
tained, calculating moreover the useful effect of
the engine, and expressing it under the different
forms already indicated, we form the following
Table :
PRACTICAL FORMULiE. 379
Effects of a locomotive of 65 cubic feet of vaporizatiouy
with a had of 56 torn gross, on a level, tender included.
M =56 tons g^oss, tender included, (10 car-
riages and the tender) ;
i; = 25*10 miles per hour;
u. £ = 1411 tons gross drawn 1 mile per hour,
tender included ;
u. E. in HP. . . = 23 horses ;
Q. CO. pr. t. pr. m. = '47 fb. per ton g^oss per mile, tender not
included ;
Q. wa. pr. t. pr. m. = *052 cuhic foot per ton g^oss per mile,
tender not included ;
u. E. 1 ft. CO. . . = 2*36 tons gross drawn 1 mile, tender in-
cluded ;
u. £. 1 ft. wa. . .= 21*70 tons gross drawn 1 mile, tender
included ;
Q. CO. fr. 1 HP. . = 26-60 fts. ;
Q. wa. fr. 1 HP. . = 2-880 cubic feet;
u. E. 1 ft. CO. in HP.= *038 horse ;
u. E. 1 ft. wa. in HP.= '347 horse.
Maxima effects of the same engine.
M' =161*5 tons gross, tender included (31
carriages and tender) ;
v', = 16*20 miles per hour;
u. E =2616 tons gross drawn 1 mile per hour,
tender included ;
u. E. in HP. . . = 42 horses ;
Q. CO. pr. t. pr. ra. = *24 ft. per ton gross per mile, tender not
included ;
Q. wa. pr. t. pr. m. = '026 cubic foot per ton gross per mile,
tender not included ;
u. E. 1 ft. CO. . . =4*38 tons g^oss drawn 1 mile, tender in-
cluded ;
380 CHAPTBR XII.
m E. I ft. wa. . . = 40'25 tons groes dnwn 1 mile, tender
indoded;
Q. CO. fir. 1 HP. . = 14-29 ■».
Q. wa. fir. 1 HP. . = 1553 cubic foot;
u. £. 1 ft. CO. in HP.= '070 hone ;
n. £. 1 ft. wa. in HP.= *644 hone.
To give a second example of this calculation, we
will suppose the railway to have 7 feet of width of
way, like the Great Western Railway^ and seek what
will be the velocity of the engines of medium force,
in use on that line, under the same circumstances
as we have just examined relatively to a railway
of about 5 feet of width of way.
We will suppose then a locomotive of 120 cubic
feet of vaporization, at the velocity of 25 miles per
hour, with the following proportions: cylinders 14
inches or 1*17 foot in diameter, stroke of the piston
16 inches or 1*33 foot, wheels 8 feet in diameter,
not coupled, weight 18 tons, friction 270 fts., blast-
pipe 3*14 inches in diameter, total or absolute
pressure in the boiler 80 lbs. per square inch, and
consumption of coke in the same time 1050fts. or
8*75 lbs. per cubic foot of water vaporized. More-
over, by reason of the width of the way, we will take
the surface of the largest waggon of the train at 100
square feet, the average surface of a waggon at 56
square feet, and the weight of the tender at 10 tons.
Seeking then by the same calculation as before,
what effects this engine is capable of producing, first
in drawing a train of 60 tons gross, tender included,
PRACTICAL FORMULiE. 381
which makes 50 tons without the tender, and after-
wards in drawing its maximum load, we obtain the
following results :
Effects of a locomotive of \20 cubic feet of vaporization^
with a load of^O tons gross, tender included*
M =5 60 tons gross, tender induded (7 car-
riages and the tender) ;
V = 34*75 miles per hour;
a. £ = 20S5 tons gross drawn 1 mile per hour,
tender induded ;
n. £. in HP. . . =: 33 horses ;
Q. GO. pr. t. pr. m. = *60ft. per ton gross per mile, tender nai
induded ;
Q. wa. pr. t. pr. m. =: *069 cubic foot per ton gross per mile,
tender not induded ;
n. £. 1 ft. CO. . • = 1*99 ton gross drawn 1 mile, tender in-
duded;
u. £. 1 ft. wa. . . = 17'38 tons gross drawn 1 mile, tender
included :
Q. CO. fr. 1 HP. . = 31-48 tts. ;
Q. wa. fr. 1 HP. . = 3-597 cubic feet ;
u. £. 1 lb. CO. in HP.= -032 horse ;
tt. £. 1 ft. wa. in HP.=: -278 horse.
Maxima effects of the same engine.
M' = 147 tons gross, tender induded (20 car-
riages and the tender) ;
v' = 25*55 miles per hour;
u. £ = 3756 tons gross drawn 1 mile per hour,
tender included ;
Q. £. in HP, . . = 60 horses ;
382 CHAPTER XII.
Q. 00. pr. t. pr. m. = *301b. per ton grom per mile, tender moi
mdiided;
Q. wa. pr. t. pr. m. = '034 cubic foot per ton gross per mfle,
tender moi indnded ;
n. £. 1 ft. CO. . . = 3*58 tons giosB drswn 1 mile, tender in-
dnded;
n. E. 1 ft. wa. . . = 31'30 tons gross drawn 1 mik, tender
indnded ;
Q. CO. fir. 1 HP. . = 17-47*8. ;
Q. wa. fir. 1 HP. . = 1997 cabic foot ;
n. E. 1 ft. CO. in HP.= *057 horse;
n. £. 1 ft. wa. in HP.= -501 horse.
The velocity of the same engine, drawing its
tender alone, would be 43*28 miles per hour;
which would be the maximum of velocity that this
engine could attain.
It is visible, in these examples, that the above
formulae present no difficulty, and that it is merely
necessary to preserve in them the homogeneity of
the measures employed.
ARTICLE IV.
BXPBBIMBNTS ON THB VBLOCITY ANd LOAD OP THB
ENGINES.
That a precise idea may be formed of the degree
of accuracy attainable by the formulae which we have
just given, and that besides, in case of need, calcu-
lations may be grounded on material facts, we will
here give a series of experiments, which we under-
PRACTICAL FORMULiE. 383
took with a view to know the velocities at which the
engines draw different loads, in their ordinary and
regular work.
These experiments were made on the Manchester
and Liverpool Bailway, of which this is the section,
such as it results from a survey made in the month
of August, 1833, by Mr. J. Dixon, then engineer to
the Company. We give only that part of it which
is traversed by the locomotives. There are besides,
under the town of Liverpool, three tunnels, worked
by stationary engines.
The railway beginning at the Liverpool station,
and ending at that of Manchester, traverses the
following distances and inclinations :
'53 mile, level.
5*23 — descent nrffT
1*47 — ascent ^
1-87 — level.
r39 — descent -^
2'41 — descent ttVt
6*60 — descent -^^
5'62 — ascent t^W
4-36 — ascent TaVr
29*48 miles.
During the experiments in question, the .velocities
were carefully taken by noting, in minutes and
seconds, the moment of passing by every quarter of
a mile on the road. The quarter miles are marked
by numbered posts. At the same moment the
1
384 CHAPTER XII.
pressure of the steam in the hoiler and in the blast-
pipe was also observed.
The weight of the waggons was taken exactly, in
tons, hundred-weights, and pounds ; but we express
it, for greater convenience, in tons and dedmals of a
ton. The tenders of the engines were not weighed ;
they are quoted at their average weight during
the trip ; namely, 5*5 tons when water is taken on
the road, and only 5 tons when that is not the case.
The carriages containing passengers could not be
weighed, because the regulations of the railway do
not admit of that delay ; but we have here inserted
their average weight, as well as that of the private
carriages and trucks.
The state of the weather is noted, because it is
well known that a wind a-head, and, above aU, a side
wind, which presses the flange of the wheels against
the rails, increases the resistance of the train ; and
the date of each experiment is given as a point of
verification.
The following Table contains the results of these
experiments. The first column gives the description
of the engine and its load, the second indicates
the inclination of the portion of road traversed by
the train, the third and fourth show the effective
pressure of the steam in the boiler and in the blast-
pipe, such as they were observed at the moment of
the experiment. In the fifth we have given the
opening of the regulator at the time, as a fracticm
PRACTICAL FORMULA. 385
of its total size; but it must be added that the
engine Star, on which we had caused graduated
divisions to be marked, was the only one which
admitted of measuring the opening with precision.
In the other engines, the handle of the regulator did
not turn on a graduated circle, and therefore we
could only set down the degree of the opening as it
might be estimated by the eye. The sixth column
of the Table contains the velocity of the engine,
such as it was observed, and, in fine, the following
column gives the result of our formula for the case
considered.
To perform the calculation relative to each en-
gine, we use the determinations developed Chap. X.
Thus we attend to the variation of the vaporization
with the velocity of the motion, according to what
has been indicated. We take account of the habitual
blowing of the safety-valves during the progress, for
all the engines, except the Star, which was not
liable to such loss ; and it will be recollected that
this loss amounts on an average to *05 of the total
vaporization of the boiler. In the experiments
made on the inclined planes, we likewise deduce
the considerable loss which then manifests itself at
the valves of all the engines, and of which the
valuation has been seen for every case. We take
account too of the water carried away with the
steam without being vaporized, or, according to the
technical term, the prime water; and for these
divers dements of calculation, we refer to the
2c
386 CHAPTER XII.
details oontained in Chapter X., without repeating
here, for each engine, the determination which
concerns it. Relatively to the absolute size of
the regulator of the engines, we refer likewise to
the chapter where that subject will be specially
treated; in that place will be found, for each en-
gine, the dimensions of the steam-ways, and conse-
quently of the orifice of the regulator when it is
entirely open. But as the greater or less opening of
the regulator has no other action than that of pro-
ducing directly the blowing of the valve, or indirectly
the reduction of vaporization in the boiler, and as
the use we make of the effective vaporization in our
formulse already comprehends those two efiects, we
merely indicate, in the fifth column, the opening of
the regulator, by a fraction of its total size ; which
will suffice for the finding of its absolute size, should
it appear necessary. Finally, all the engines worked
with more or less lead of the slide^ which is a
particular disposition that we shall treat of in
Chapter XVI.; but as we shall then find that
this lead was very slight, and as its efiects besides
are already found comprised in the loss of water by
priming^ such as we have determined it, we will
avoid complicating our calculations with this ad-
dition. We shall make an exception however in
this respect for the engine Vesta, because, in that
engine, the loss by priming had been determined
for another lead of the slide than that at which
it worked in the experiment which we are about
PRACTICAL FORMULA. 387
to relate. For this case then we shall take ac-
count of the lead of the sUde as will be indicated
Chap. XVI.
In making the comparison between the observed
and the calculated velocities, attention must be paid
to several circumstances.
1st. There is reason to believe that, when engines
work at less pressure in the boiler, they are liable to
less loss by priming. As, therefore, we have made
use in this respect of the mean determination for
each engine, it is in general to be expected that in
the cases of low pressure, the calculated velocities
will be found somewhat too small, and that, in the
contrary case, they will be rather too great.
2d. The direction of the wind must necessarily
have some influence on the velocity of the train.
3d. When the water contained in the tender is
very hot, since its heat diminishes continually as the
journey advances, it will most commonly happen
that the engine will vaporize more water, and con-
sequently assume a greater velocity at the beginning
of the experiment than at the end of it.
4th. The difierences arising fix)m the three pre-
ceding circumstances, become easily compensated
by the irregularities in the vaporization of the
engine; and these are inevitable, as well from the
greater or less attention of the engine-man, as on
account of the sudden slackening which the vapor-
ization is subject to, ev^ time it becomes necessary
to heap up the fire or to refill the boiler. Thus,
(
388 CHAPTER XII.
since the observed velocities result from the actual
and variable vaporization of the boiler, whereas the
calculated velocities are determined from the mean
vaporization of the engine, supposed to be uniform
throughout the trip, there must necessarily occur,
from time to time, considerable differences between
the calculation and the observation; but it will
readily be perceived that these differ^ioes depend
on the irregularities of the vaporization, on ob-
serving that, in the same trip, the engine often
assumes its greatest velocity at the moment when
the gravity opposes the greatest resistance, or that
two portions of the line, on which the gravity is
sensibly the same, are traversed with velocities very
difierent. However, were the experiment sufficiently
prolonged, all these momentary irregularities would
disappear almost entirely.
PRACTICAL FORMULiE.
389
Eaperimenti an the velocity and the load of locomotive engines.
Date of the experiment, md
derignstioii of
tiie engibe md its load.
Stab. Cylinder
Stroke .
Wheel .
Wei(^t
Fire-box
Tubes .
Friction
14 in.
12 in.
5ft.
11-201.
49*71 Bq. ft.
279*18 sq. ft.
176 lbs.
IncUnatioD
of
the road.
Stak, Ang. 10, 1836, from liver,
to Man., with 12 wag. and
tender, 43*65 tons.
Gross yaporiz. per hour, 65*49
cubic feet, at the mean ve-
locity of 20*78 miles per
hour.
Diameter of blast-pipe, 2*36 in.
Star, Aug. 13, 1836, from Man.
to IiEver., with 9 wag. and
tender, 48*48 tons.
Gross vaponz. per hour, 62*83
cubic feet, at the mean ve-
locity of 18*79 miles per
hour.
Diameter of blast-pipe, 1*78 in.
Stae, Aug. 11, 1836, from liver,
to Man., with 12 wag. and
tender, 59*84 tons.
Gross vaporiz. per hour, 61*05
£ahic feet, at the mean ve-
locity of 18-32 miles per
hour.
Diameter of blast-pipe, 2*82 in.
Stae, Aug. 11, 1836, fhnn Man.
to Liver., with 9 waggons
loaded, 6 waggons empty,
and tender, 61*24 tons.
Gross vaporiz. per hour, 65-50
cubic feet, at the mean ve
locity of 17*46 miles per
hour.
Diameter of blast-pipe, 1-26 in.
. o
Ob-
•erved
effectire
prenure
in the
boUer.
Ob.
■erred
effeetiTe
prewure
in the
blaat-
pipe.
Ifee. per
■q. ineh.
0
0
30*0
27*1
18-0
22*6
20*2
Ibe. per
■q. inch.
27*7
26*0
280
23-8
26-4
30-0
27*0
20*5
221
32*7
31*0
24*3
M
Opening
of the
regu-
lator, in
a frac-
tion of
its total
die.
Ob-
■erred
rdoettjr,
inmilea
hour.
4-8
2*4
1*8
2*9
2*2
5-4
5*0
4*2
3-4
4-9
6-0
»»
n
n
If
f»
If
>f
•5
•5
•6
•5
•5
■5
■5
•5
milea.
23-64
20-00
2500
20-69
20*77
Calculated
Telocity,
in milea
perhoor.
21*82
23-53
18*75
19*20
20*00
20-00
24*62
16-67
20-87
22*50
20*00
18*00
15-00
21-43
16*79
18-75
mOea.
22-12
21-88
24-10
20-14
21-22
Obaerrstiona.
Weather fair and
calm.
Water in the ten
der hot.
20*82
21*89
18-83
20*23
19-66
18-65
22-00
19-97
20-85
22-27
18*77
19*74
Weather fair and
cahn.
Water in the ten
der hot.
rWeather fur and
calm.
Water in the ten
der tepid.
17*48
18-91
15-97
17-00
Weather hkt and
aim.
Water in the ten«
der cold.
390
CHAPTER XII.
Date of the ezpcrimeat, and
thm <>ngw»^ VoA its llWld
iBdinatkm
of
the road.
Stab, Aug. 9, 1836, firom Man. to
Liver., with 3 wag. loaded,
32 wag. empty, and tender,
75*05 tons.
Gross Taporiz. per hour, 68*79
cubic feet, at the mean ve-
locity of 14'45 miles per
hour.
Diameter of blast-pipe, 2 in.
With 38*58 tons
With 41-97 tons
Stak, Aug. 9, 1836, from Liver,
to ifan., with 20 wag. and
tender, 96*30 tons.
Gross vaporiz. per hour, 60*64
cabic feet, at the mean ve
locity of 17-35 nules per
hoar.
Diameter of blast-pipe, 2-82 in.
Stae, Aug. 13, 1836, from liver,
to Man., with 22 wag. and
tender, 109*68 tons.
Gross vaporiz. per hoar, 54*20
cabic feet, at the mean ve-
locity of 13-85 miles per
hoar.
Diameter of blast-pipe, 2 in.
Stak, Aag. 9, 1836, from lAver.
to Man., with 23 wag. and
tender, 120-27 tons.
GroM vaporiz. per hoar, 67*71
cabic feet, at the mean ve-
locity of 15*13 miles per
hoar.
Diameter of blast-pipe, 2 in.
fta.per
■q. laeh.
*• vrn
o
^ A
•• ^
42-3
36-0
30-0
o
d* tH,
*" TWlfT
Ob-
iatke
boOer.
Ob.
dibetive
'Opening
of the
intlie
Mart-
pipe-
0
*■ Xwsr
o
d. wH
*■ unnr
41*6
42-5
45-2
48-6
44-3
481
49-6
50-6
40*0
31*5
23*6
38*8
42*0
30*7
37-5
330
32*3
480
26*0
39*8
41*2
450
Die. per
■q. inch.
4*8
5*1
4*4
5*8
6*3
6-2
2*8
1-8
3*0
2-4
2*3
1*8
2-3
2*0
1-0
2*4
3-8
2-1
1-6
1-2
4*3
50
3*0
5-6
4-4
4*9
lator,in
tion of
its total
1
1
1
1
1
1
1
1
nulci.
16-96
17-50
14-53
16-67
16-39
17-73
911
7-28
22*85
2000
20*00
21-82
17-56
19*25
19*57
13*33
1714
15-00
12-63
12*47
16-95
15*00
1500
17*21
15-24
16*55
milei.
19-03
19-92
16-47
17*46
18-30
16-43
10*27
10-11
Weather fur ind
calm.
I
Water in the ten-
der Teiybot.
19-00
17-00
17*90
20*10
15*58
16*75
18*00
14*38
15*17
18-09
13*60
14*84
19-71
16-87
18-63
19*45
15*03
16*08
Weather frtr uJ
in the fees-
hot.
Wenther fair aad,
Water in the ftco
dor cold.
Weather lur aa^
I calm.
^ Water in the ten-
der almost cold.
1
PRACTICAL FORMULiG.
391-
Opening
Ob-
of the
Ob-
■enred
rega-
Ob-
■erred
effMliye
lator,in
•erred
Calenlated
Date o£ the experiment, and
eflfiBctiTe
preMure
a tac-
rdodty.
▼eloeity.
deaigiiiili<m of
of
prewuK
in the
tion of
inmilet
inndlea
Obacrvatiooa.
the engine and ita load.
tberoad.
in the
blaat.
ita total
per
per hour.
boUer.
pipe.
aiie.
hour.
Ibe. per
Ibe. per
miles.
miles.
■q. inch.
VxsTA. Cylmder . a 11*125 in.
Stroke ... 16 in.
Wheel ... 5 ft.
Weight... 8*71 1.
Fire-hox . . 46*00 Bq. ft.
Tubes. . . 215-66 sq. ft.
Blast-pipe.. 2-50 in.
•
Friction.. 181 fbs.
Vesta, Aug. I, 1834, from Man.
»-
^
to Liver., with 5 waggons
^WST
50
tr
30*00
30*60
Weather fur. A
loaded, 5 empty, and ten-
"•TiAnr
50
tt
34*74
31-07
moderate wind
der, 33*15 tons.
. *• ¥i¥
50
n
28*93
29*09
in favoor of the
Gross vaporiz. per hour,
55
>f
14-11
15-50 '
motion.
65-00 cubic feet, at the
0
50
n
29*00
30*18
Water in tiie ten-
mean velocity of 27*33
•• Tihrf
50
tt
28-80
2911
der Teiy hot.
miles per hour.
m
..
FiRSFLT. Cylinder . 11 in.
Stroke . • 18 in.
-
Wheel .. 5 ft.
Weight . . 8-74 t.
Fhe-box . 43*91 sq. fl.
Tubes . 317*71 sq. ft.
Blast-pipe 2*25 in.
Friction 123 lbs.
FiRBFLT, July 26, 1834, from
i»
Liver, to Man., with 8
Weather fiiir.
first-dass coaches, and
0
50
ft
1
24*00
25*09
Water in the ten-
tender, 41*40 tons.
, ^lAt
45
M
1
25*45
27*08
The engine in a
Gross vaporiz. per hour,
45
tt
1
21*29
23*96 '
bad state, losing
64*10 cubic feet, at the
••tAt
35
tt
1
21*33
24-48
water by the
tnli^ of th«
mean f^odty of 17*70
boiler.
miles per hour.
»
Weather rainy.
FiRBFLT, July 26, 1834, from
«•
—
A rather strong
Man. to liver., with 8
first-dass coaches, and
tender, 41*40 tons.
Gross vaporiz. per hour,
77*31 cubic feet, at the
mean velocity of 21*33
0
45
50*33
50*5
50*33
50
tt
tt
tt
tt
tt
•5
•5
•5
5
5
23*68
24-44
23-44
25*71
24*82
27-93
28*56
25*40 ^
26-59
25*70
wind against the
direction of the
motion.
Water in the ten-
der tepid.
The engine in a
bad state, losing
water by the
miles per hour.
^
■•
tubes of the
boiler.
392
CHAPTER XII.
•
Opening
Ob-
of the
•
Ob-
serred
regn-
Ob-
serred
effBClive
Utor^in
served
Calculated
Indinstion
effective
pressure
afinie-
relocity.
yeloatir.
designation of
of
pressure
in the
tionof
in miles
m milea
OtiliiitiiiiiB
the engine and its load.
the rood.
in the
blast-
iU total
per
perhovr.
1
boiler.
pipe.
siae.
hour.
1
lbs. per
■q. inch.
lbs. per
sq. Siidi.
miles.
miles.
1
FuBY. Cylinder . . 11 in.
i
Stroke . . .
16 in.
■
Wheel . . ,
5 ft.
)
Weight . .
. 8-20 1.
Fire-box . .
. 32*87 sq. ft.
Tubes . .
. 267-84 sq. ft.
Blast-pipe .
2-156 in.
Friction . .
, 96tbs.
'
FtJBT, July 24, 1834, from Man.
to Liver., with 10 wag. and
tender, 48-80 tons.
Gross vaporiz. per hour, 57*46
cubic feet, at the mean ve-
locity of 18*63 miles peri
hour.
d-rATT
0
••tAtt
55
55
55
67
55
55
n
n
n
ff
>i
-75
-75
•75
1
•75
•75
21-43
22-00
18-62
15-00
17-50
18^46
20-73 ^
21-72
18-57
8-00 '
20-10
18-80
Weather feir. A
rather sCroa;
side wind St ia-
tervals.
Water in the tfi-i
doreold.
1
Fury, July 24, 1834, from Liver,
to Man., with 10 wag. and
tender, 56-16 tons.
Gross vaporiz. per hour, 54-45
cubic feet, at the mean ve-
locity of 19-67 miles per
hour.
0
55
65-5
55
55
55-5
55
n
M
n
n
ft
n
•75
1
•75
•75
•75
•75
1800
6-31
17-14
23-28
21-82
2117
20-14'
6-74
18-82
20-50 ^
17-45
18-07
Weather fiurns
Water in the to^
deroold.
1
Lbsdb. Cylinder . 11 in.
Stroke . . 16 in.
Wheel. . . 5 ft.
Weight . . 7-07 t.
Fire-box . . 34-57 sq. ft.
Tubes . . . 267-84 sq^ ft
Blast-pipe . 2-156 in.
■
»
Friction . . 85 lbs.
Lbbds, Aug. 15, 1834, from Liver.
»•
•<
to Man., with 20 wag. and
tender, 88-34 tons.
^-rrfn
54
tt
•75
20-72
22-26
• ^^ ^ ^
0
54-75
t»
-75
18-26
20-25
Weather calm.
Gross vaporiz. per hour, 63-18
* ^ rb
54
»f •
-75
24-00
23-00 >
Water in the tcB-
S 1_ *A
cubic feet, at the mean
•- "nAnr
54
>f
-75
20-34
19-00
der scarcely tr-
PW.
velocity of 18*63 miles per
^Wkt
54
f»
•75
18-82
19-60
hour.
h>
•
^
PRACTICAL FORMULA.
393
Opening
Ob-
of the
Ob-
■erred
regu.
Ob-
awed
eflectiTe
lator,in
■erred
Calenlated
Date of Um eipcrisMot, and
dwignatwia of
f|^Hp>^^f^^
eflbcliTe
in the
afrae-
velocity,
in miles
velocity,
in milea
ol
preaauie
tion of
^^a » *
the engine and ita load.
Iheioad.
in the
blaat-
ita total
,P»
per hour.
bailer.
pipe.
■iae.
hour.
Iba. per
Iba. per
milea.
milei.
■q. inch.
■qiindi.
Lkbds, Aug. 15, 1834, from Mao.
p"
"
to Liyer., with 8 wag. and
tender, 39-88 tons, half
d.:iAT
51-5
»»
-76
24-54
27*16
Weather Ciir and
the road, and 7 wag. and
d-TiAnj
46-5
»
•75
30-00
28-11
calm.
tender, 35-15 tons, &e reit
, *• »*T
46-5
»»
■75
25-31
25*25
Water in the ten-
of the way.
4 — -w-^
O
46-5
fi
-76
22-50
27-75
der very hot.
GroM Taporiz. per hour, 68-82
•- ^
48-5
»f
I
10-00
14*97
One wag. left be-
cubic feet, at the mean
•■ Tf^
54
i>
•75
25-71
26-20
hind half way.
▼elodty of 21-99 miles pei
hour.
>.
a
Vu LC AN. - Cylinder 1 1 in.
Stroke . . 16 in.
Wheel • . & ft.
Weight . 8-34 t
Fire-box 34*45 sq. ft
Tubes . . 267-84 sq. ft.
Blast-pipe 2-156 in.
Friction . 125 ibs.
Vulcan, July 22, 1834, from Man.
>»
^
to Uver., with 9 first-
dass coaches and tender,
39-07 tons.
Gross Tiq^riz. per hour,
60*60 cubic feet, at the
• •• A
57-5
•
»f
1
11-42
11-22 '
Weather calm.
Water in the tm-
der hardly tq>id.
mean velocity of 22*99
miles per hour.
>•
■^
Atuws. Cylinder . 12 in.
Stroke . . 16 in.
Wheel ... 5 ft.
Weight . . 11-40 t.
Fire-box . 57-07 sq. ft.
Tubes . . . 197-25 sq. ft.
Friction . . 139 ibs.
Atlas, July 23, 1834, fix>m Liver,
to Man., with 40 wag. and
tender, 195-5 tons.
o
53
53-5
M
14-12
9-23
13-50
10-05
Weather feir and
calm.
Water in the ten-
Gross Taporiz. per hour, 43-81
cubic feet, at the mean ve-
locity of 8*99 miles per
hour.
53
55
54*5
ft
rf
»>
16-21
800
5-87
14-00 ^
8-38
9-60
der cold.
The encine was
assisted at start-
ing by two other
BUst-pipe, 2-94 in.
>.
-
engines.
396 CHAPTER Xlll.
the engine with an indeterminate load or velocity,
and the two others to the production of the max-
imum of useful effect.
From hence then it results that, according as
either of these general analogies he taken to deter-
mine one or other of the dimensions of the engine,
the following are the questions that it may be pro^
posed to resolve :
«
1st. To determine, either the heating surface of the
boiler, or the diameter of the cylinder, or the
length of the stroke of the piston, or the diameter
of the wheel, that the engine may draw a given
load at a desired velocity ;
2d. To determine, either the heating surface of the
boiler, or the diameter of the cylinder, or the
stroke of the piston, or the diameter of the wheel,
or, in fine, the pressure in the boiler, that the
engine may acquire a desired velocity, or draw
a given load, producing at the same time its
maximum of useful effect ;
3d. To determine the combined proportions proper
to be given to the divers parts of the engine, to
enable the engine to fulfil divers simultaneous
conditions.
Each of these three enunciati<m8 visibly compre-
hends a series of distinct questions, which we shall
resolve successively. We shall therefore first suppose
that it is required to determine one of the dimensions
of the engine, according to the general condition of
CHAPTER Xm.
OF THE PROPORTIONS OF LOCOMOTIVE ENGINES.
Sbct. I. Of the divers problems which occur in the
construction of locomotive engines.
In the preceding chapter, we have sought the effects
producible by a locomotive engine already con-
structed, or whose dimensions are determined; we
are now about to determine, on the contrary, what
should be the proportions of a locomotive engine,
as yet unbuilt, in order to obtain from it desired
effects.
In this state of the question, the quantities given
h priori are the load of the engine for a known
velocity, or else its velocity or its load corresponding
to the maximum of useful effect ; and the unknown
or indeterminate quantities are the heating surface
of the boiler, the diameter of the cylinder, the length
of the stroke, the diameter of the wheel, and the
pressure in the boiler.
On the other hand, we have demonstrated in the
preceding chapter, that there exist between these
divers quantities, known or unknown, three general
analogies expressed by the equations (1 bis), (4 bis),
and (5); the first relating to the general effects of
398 CHAPTER XIII.
Substituting then in this equation for v and M, the
given velocity and load, putting likewise, for the
dimensions of the engine, their values which may
be taken arbitrarily, and, in fine, putting for F the
presumed friction of the engine, such as we have
given the means of valuing it in Chapter VIII., we
shall obtain the effective vaporization which the en-
gine ought to have, in order to fulfil the condition
prescribed.
Thence must afterwards be deduced the total or
gross vaporization of the boiler. Now we have
found that in locomotive engines of the present
construction, the efiective vaporization is to the
total vaporization in the ratio of the numbers '75
and 1. Therefore the total vaporization of water,
corresponding to the efiective vaporization S, is
S'= A= 1-33 S.
•75
And as moreover, in certain engines, there is yet
lost, during the motion and by the safety-valves,
^ of the total water vaporized, it follows that for
those engines, we shall have the definitive total
vaporization of the boiler, on multiplying the
quantity just obtained by the factor 1 '05 ; so that
the total vaporization will then be
S'=1'05X 1-33 S= 1-40 S.
Thus will then be attained the knowledge of the
total vaporization necessary to the production of the
desired efiects. This vaporization will be such as
OF THE PROPORTfONS OF THE ENGINES. 399
the engine ought to produce at the given velocity v,
and since we have seen that the vaporization varies
in the ratio of the fourth roots of the velocities, it
follows that at the velocity of 20 miles per hour,
the same engine ought to be capable of vaporizing a
quantity of water expressed by
1-40 SX(^)*-
Consequently, if it be desired to conclude from
hence the heating surface which the boiler ought
to have, it will suffice to refer to the results which
we have obtained in Chapter X., namely: that at
the velocity of 20 miles per hour, each square foot
of total heating surface produces a vaporization of
•200 cubic foot of water per hour. Thus the total
heating surface necessary to produce the effective
vaporization S, at the given velocity v, will be
•20 V t; / V v /
If the given velocity v differ but little from 20
miles per hour, or if a very great degree of precision
is not required, we may, in this expression, neglect
the term
and be satisfied with taking the heating surface
equal to the quantity 7S.
It appears at the same time that, in order to
obtain immediately the effective vaporization of a
400 CHAPTBR XIII.
given boiler, we may limit the calcalation to taking
i|^ of the total heating surface, exin'essed in square
feet; and the result will he the vaporization ex-
pressed in cubic feet of water per hour. This sum-
mary method may be used in practice, as an ap-
proximation.
Sect. III. Of the diameter of the cylinders^ necessary
that the engine may draw a given load at a given
velocity.
K, in planning an engine, the vaporization which
the boiler is to have has been previously settled,
desired effects may yet be attained by
for that purpose one of the other dimaisions of the
engine.
For instance, the diameter of the cylinders, which
would enable the engine to fulfil the prescribed con-
ditions, may be sought. To obtain the solution of
this problem, it evidently suffices to solve equation
(1 bis) with reference to d, which is the diameter of
the cylinder, and we have
^ D i + «
9
C5So-frc-(-r^-(*±'>"^'"— '-i^ - w
Substituting in this equation, for S, v, M, D and
/, the values that have been previously fixed on,
introducing for F the presumed fiiction of the
aigine, such as we have found it in Chapter VIII.,
and for pv the pressure in the blast-pipe, resulting
OF THE PROPORTIONS OF THE ENGINES. 401
from the proportions adopted, we shall obtain in the
second member the value of d^, taking the square
root of which we have definitively the value of rf,
or the diameter of the cylinder expressed in feet.
It is to be remarked that the proposed problem
will be possible only when
5280-/— cTTT»-7>(*±^)^±^^-^'-^TT5-'
or
S >5280 ^(1 + «)^ [](*±^)M±^ + i«r 2+ j-|y] ;
for otherwise the second member of the equation
would become negative, and the value of d would
be imaginary. This condition is readily explained
on referring to the general value of the vaporization
necessary to draw the load M at the velocity v.
This general value is, as has been seen, according
to equation (7),
5280
and it is manifest, on the mere inspection, that if
the value supposed for S did not fulfil the condition
indicated above, the vaporization would be. insuf-
ficient to draw the load M at the velocity v, what-
ever might be the diameter chosen for the cylinder.
The impossibility of the problem would arise then
from the values adopted for S, M and v being in-
compatible with each other; but on taking a suf-
ficient value for S, the required solution will be
easily attained, by me^ns of the preceding formula.
2 D
402 CHAPTER xni.
Sect. IV. Of the length of the stroke of the piston^
requisite for the engine to draw a given load ai a
given velocity.
If, besides the vaporization of the boiler, the
diameter of the cylinder has also been fixed upon,
but that nothing has been decided relative to the
stroke of the piston, the value of this undetermined
quantity may still be obtained, such as to enable
the engine to fulfil the desired conditions.
To obtain the length of stroke proper for an
engine, entirely determined in other respects, in
order that it may draw a desired load at a given
velocity, it will be sufficient to resolve equation
(1 bis) with reference to /, which will give
9
This equation then will solve the question, and it
will be remarked that, to prevent I from becoming
a negative quantity, the value of S must fulfil the
same condition as in the preceding inquiry, which
is explained in the same manner.
The presumed friction F of the engine, and the
pressure p'v in the blast-pipe, which are to be sub-
stituted in the equation, will be obtained as it has
been said in the last section.
OF THE PROPORTIONS OF THE ENGINES. 403
Sect. V. Of the diameter of the wheels necessary
far the engine to attain a desired velocity with
a given load.
In fine, it may still occur that from different
considerations all the other proportions of the en-
gine have been decided on, and that with these
proportions it be required to know, what diameter
should be given to the propelling wheel of the
engine, that it may acquire a desired velocity with
a ^ven load.
The quantity D in this case becomes the object of
determination of the problem, and its value will
again be drawn from equation (1 bis), namely :
^-ITi--r-T-T-T-4-— —Z — T--W
5280 '
/rc-7-Tn-ir-(*±^>^+^-""'-TT?
It will be remarked that this equation, like the
two preceding ones, is also subject to the condition
that the vaporization adopted for the engine be not
incompatible with the load and the velocity which
are intended for it at the same time; and it is, of
course, needless to add, that if the value of D re-
sulting from this formula should be found too large
or too small to be applicable in practice, the solution
obtained must be regarded merely as satisfying the
algebraic equation, but by no means as solving the
practical problem in the manner it ought to be
understood.
404 CHAPTER XIII.
Sect. VI. Of the vaporization^ or of the heating
surface a locomotive engine ought to have^ in order
to acquire a given velocity, producing at the same
time its maximum of useful effect.
The four questions which have occupied us thus
far, have had in view to determine one or other
of the dimensions of the engine, from equation
(1 bis), that is, from the condition that the engine
draw any given load whatever, at a given velocity.
But we are now about to suppose that it is required
to determine the dimensions of the engine, not from
its effects with any given load, but from the con-
dition that it produce its maximum usefrd effect,
either at a given velocity, or with a given load;
and as the relation between the dimensions of the
engine and its maxima effects is expressed by the
two equations (4 bis) and (5) , namely :
,^ JL s^ D I
^ *5280 • rf« • /+c 'fi + yP'
to these we must have recourse in order to attain
the solution sought.
Suppose, then, it be required to determine the
vaporization S, or, in other words, the heating
surface of the engine, according to the conditiqn
that it produce its maximum of usefrd effect at a
certain given velocity v\
OF THE PROPORTIONS OF THE ENGINES. 405
It is clear, then, that the value of S must he
derived from equation (4 bis) , which will give
S=5280 L±l , ^' . ^' (" -f P) ..... (11)
/ D \q '
This equation will make known the effective vapor-
ization sought, as soon as v and the dimensions
of the engine shall be replaced by their values
supposed fixed or chosen beforehand; and from
it will be concluded, as in Sect. i. of this chapter,
the total consumption of water in the boiler, and
consequently the heating surface necessary to obtain
the desired effect.
It will be remarked that, as equation (5) furnishes
no relation between the vaporization S and the
maximum load of the engine, the vaporization can-
not be determined directly, from the condition of
the engine drawing a certain given load, producing
at the same time its maximum useful effect. It is
evident, indeed, that as this condition depends
entirely on the effort the engine is capable of ex-
erting, and is altogether independent of the velocity
of the motion, the question is to be solved only by
seeking the pressure of the steam in the boiler,
capable of producing the determined effort; and
consequently it is in the next problem that its solu-
tion win be found.
406 CHAPTER XIII.
Sect. VII. Of the pressure in the boiler necessary
for the engine to draw a given load^ or acquire a
desired velocity^ producing at the same Hme its
maximuta of useful effect.
If the maximum load of the engine, or, in other
words, the load it should draw when producing its
maximum of useful effect, have been previously
decided on, and if it be desired to know what
ought to be the pressure in the boiler, to enable the
engine to draw that maximum load, it is clearly to
equation (5) that recourse must be had, since that
is precisely the equation which gives the relation
between the known and unknown quantities of the
problem under consideration.
Resolving then this equation with reference to P,
which is the pressure in the boiler, we obtain
This formula then will make known the pressure P.
It is to be observed only that this equation con-
tains two terms pv and uv^^ functions of the
minimum velocity of the engine, which is not given
h priori^ but which is, on the contrary, to result
from the knowledge of P, according to the equation
(1 bis), when that quantity P shall be determined.
This circumstance therefore will render it necessary
to operate here in the same manner as we have
already indicated relatively to equation (1), in the
OF THB PR0P0ETJ0N8 OF THE ENGINES. 407
preceding chapter; that is to say, the operation
must be performed by successive approximations.
A supposition therefore must first be made as to the
probable value of tr\ and having calculated, with that
supposition, the value of P, it must be ascertained,
by seeking the velocity of maximum useful effect for
the pressure P and the known vaporization S of the
engine, whether that vdocity be too remote from
that whidi was supposed for the finding of P. If
the difference between the two is trifling, this first
solution will suffice, and the value thus obtained for
P may be adopted. If, on the contrary, th^ velocity
of maximum useful effect, resulting from the values
of P and S, differ from the supposition originally
made, too much to warrant placing confidence in the
result, then the calculation must be begun anew,
introducing into the equation (12) the velocity v ob-
tained by this first approximation, and thence will be
deduced a new value of P more approximate than the
first. This would lead, if required, to a third ap-
proximation ; but with a little experience, two trials
will always lead to a value of P sufficiently near for
practical uses. The problem therefore may be
somewhat long to s(dve, but can present no sort of
difficulty.
The solution thus obtained will give the total or
absolute pressure of the steam in the boiler, ex-
pressed in pounds per square foot; that is, ex-
pressed generally in units of the species of those
which are determined by the homogeneity of the
408 CHAPTER XIII.
equations, as has been explained in Sect iv. of the
preceding chapter.
Instead of determining the pressure in the boiler,
as we have just done it, that is, according to the con-
dition that the engine draw a given load, producing
at the same time its maximum of useful effect, we
may likewise determine that pressure, according
to the condition that the engine shall, with a iSxed
vaporization, attain a certain given velocity, pro-
ducing also its maximum of useful effect.
It will then be from equation (4 bis) that the
value of P must be drawn, which gives
5280 ' q ' l+c' d^r f/ q ^ ^
And substituting in this equation the value of the
divers dimensions of the engine, we have the
pressure in the boiler, which, for a given vapor-
ization, will make the engine assume the desired
velocity v\ producing at the same time its maximum
useful effect.
Sect. VIII. Of the diameter of the cylinder^ or of
the stroke of the piston^ or of the diameter of the
wheels necessary that an engine may assume a
desired velocity or draw a given loady producing
also its maximum useful effect.
It has been seen in the two preceding problems,
that if the engine is required to assume a given
OF THE PROPORTIONS OF THE ENGINES. 409
vdocity, producing at the same time its maximum
of useful eflfect, there are two ways of attaining that
»xd : either by determining the vaporization neces-
sary for the producing of that effect, or by assuming
any vaporization, and then determining the pressure
in the boiler proper to obtain the desired velocity.
We have just seen likewise, that if it be wished to
render the engine capable of drawing a certain given
maximum load, that end may be attained by deter-
mining, from equation (12), the pressure which
ought then to be produced in the boiler.
But besides these means of attaining the desired
effects, there are yet three other ways, which consist
in adopting arbitrarily the vaporization of the engine
and the pressure in the boiler, and then determining
either the diameter of the cylinder, or the stroke of
the piston, or the diameter of the wheel, according
to the condition proposed to be fulfilled.
Suppose then that the vaporization of the engine
and the pressure of the boiler be already fixed by
other considerations, and that it be required of the
engine to produce its maximum useful effect at a
certain fixed velocity v. Then it will clearly suffice to
resolve the equation (4 bis) with reference to d, to /,
or to D, according to which of those three quantities
it is wished to determine from that condition. We
shall have then
"^ -5280 • /+c • J • r ^' ^7^' • • • • ^*^^
or
410 CHAPTBB XIII.
,_ 1 /IDS 1 „.v
6280 /+c .^ rf» t/ «^p ^ ^
or ,
D=528oLtf . jd2/. ^ . (- + P) (16)
We may therefore choose one of these three solu-
tions ; and introducing into the equations for S, P,
and the dimensions of the engine, their values pre-
viously decided on, we shall obtain the value of
those dimensions which shall have been left to
determine according to the prescribed condition.
If, instead of laying down the condition th&t the
engine acquire the velocity v producing also its
maximiun useful effect, we, on the contrary, impose
the condition that it draw a certain given maximum
load M^, then the problem will be the same as the
preceding, with the exception that M' will be given
instead of v. Kecourse therefore will be had to
equation (5), which, resolved successively with refer-
ence to (2, I and D, will give
or
F
(k±g)ye±gm'^m/^+
or, in fine,
JJ— j—r . = . . . (i»;
1+*
OF THB PROPORTIONS OF THE ENGINES. 411
As these equations still contain the terms f^v and
uv"^^ which are functions of the velocity v\ and as
the latter is not yet known, but must on the
contrary result from the previous knowledge of d, I
or Dy the proceeding here will be by successive
approximations, as we have indicated above, in
Sect VII.
Sect. EX. Of the combined proportions to be given
to the parts of an engine, to enal}le it to fulfil
divers simultaneotLS conditions.
In all the preceding problems we have supposed
that all the dimensions of the engine, except one, are
assumed at will, and that this one dimension is
afterwards determined according to some condition
imposed as to the work of the engine. But as in
the general problem of the constructicm of an
engine, there are five indeterminate quantities,
namely: the heating suifaoe, or, in other words,
the vaporization, the pressure in the boiler, the
diameter of the cylinder, the length of the stroke of
the piston, and the diameter of the wheel, it is
evident that five simultaneous conditions may be
prescribed, for the engine to fulfil, and that on
determining each of the said dimensions according
to those conditions, the engine will be capable of
fulfilling them all successively, according to the
circumstances in which it is placed.
The conditions that may be prescribed, to deter-
412 CHAPTER XIII.
mine the dimensions of the divers' parts of the
engine, consist in fixing the different effects it
ought to produce under certain circumstances ; and
these effects themselves depend on three quantities
that may be assumed at will; namely, the velocity for
any given load whatever, the velocity of maximum
useful effect, and the maximum load, or load of
maximum useful effect.
As many as five values then of these different
quantities may be assumed, and the five dimensions
of the engine may be determined according to them ;
or four only of those values may be assumed, and
four of the dimensions of the engine determined
from them, the fifth then remaining to be chosen
arbitrarily; or, in fine, three or two, or even one only
of those conditions may be assumed, and the same
number of dimensions determined, the others re-
maining either to be taken arbitrarily or to be de-
termined from considerations of a different nature.
It is obvious that a considerable number of
problems may be proposed on this subject; but
they never present any difficulty. It will suffice,
in effect, to recur to equations (1 bis), (4 bis), and
(5), and to express that they exist at the same
time, for the given values of the quantities M, t;,
M', v\ Then will be drawn firom them, by elimina-
tion, the value of each of the required dimensions of
the engine.
We will not undertake to solve all the problems
that may be thus proposed ; but to show the manner
OF THE PROPORTIONS OF THE ENGINES. 413
of the proceeding, we will choose one or two among
those which may occur most frequently.
Suppose it be desired to build an engine capable
of drawing, on a given inclination, a certain deter-
mined maximum load M^ and, at the same time, of
acquiring on another inclination, a certain given
velocity v, with another load M likewise known.
We have then at the same time the two equations
(4 bis) and (1 bis), or
M'=- - — l!i — --(p-^-yt,') - i- /_!_-+ tii,'«+^\,
These may, consequently, be used to determine, for
instance, the diameter of the cylinder from the first
condition, and the heating surface from the second.
The first equation therefore must be resolved with
reference to d, and the second with reference to S.
This is what we have already done in the Sections
VIII. and II., having obtained the equations (17)
and (7), namely:
^-(^^»>7- V^p^p'^ (l^T)
S-5280^%(l + 8)^[(*±^)M±^ + iii^+-jl^+^.^(»+p+y^)].^^
Thus, introducing into equation (17), the given
value for M', we first deduce the value of d, as
has been explained Sect. viii. ; and then sub-
404 CHAPTER XIII.
Sect, VI. Of the vaporization^ or of the heating
surf ace a locomotive engine ought to havCj in order
to acquire a given velocity, producing at the same
time its m^ojdmum of useful effect.
The four questions which have occupied us thus
far, have had in view to determine one or other
of the dimensions of the engine, from equation
(1 his), that is, from the condition that the engine
draw any given load whatever, at a given velocity.
But we are now about to suppose that it is required
to determine the dimensions of the engine, not from
its effects with any given load, but from the con-
dition that it produce its maximum useful effect,
either at a given velocity, or with a given load;
and as the relation between the dimensions of the
engine and its maxima effects is expressed by the
two equations (4 bis) and (5) , namely :
,^_i s^ D I
to these we must have recourse in order to attain
the solution sought.
Suppose, then, it be required to determine the
vaporization S, or, in other words, the heating
surface of the engine, according to the conditiqn
that it produce its maximum of useful effect at a
certain given velocity v\
OF THE PROPORTIONS OF THE ENGINES. 405
It is clear, then, that the value of S must be
derived from equation (4 bis), which will give
S=5280^-f . ^'9v' (-+P) (H)
This equation wiU make known the effective vapor-
ization sought, as soon as v and the dimensions
of the engine shall be replaced by their values
supposed fixed or chosen beforehand; and from
it will be concluded, as in Sect. i. of this chapter,
the total consumption of water in the boiler, and
consequently the heating surface necessary to obtain
the desired effect.
It will be remarked that, as equation (5) furnishes
no relation between the vaporization S and the
maximum load of the engine, the vaporization can-
not be determined directly, from the condition of
the engine drawing a certain given load, producing
at the same time its maximum useful effect. It is
evident, indeed, that as this condition depends
entirely on the effort the engine is capable of ex-
erting, and is altogether independent of the velocity
of the motion, the question is to be solved only by
seeking the pressure of the steam in the boiler,
capable of producing the determined effort; and
consequently it is in the next problem that its solu-
tion will be found.
41G CHAPTER XIII.
calculatioii then would have remained entirely the
same, and the solution would obviously not have
presented more difficulty.
As a second example, we will suppose it be re-
quired to construct an engine, csqp^le of drawing,
1st, a certain given load M. at a desired velocity v.,
on a plane of known inclination, the gravity on which
shall be expressed by ^, ; and 2ndly, another given
load M, at a velocity Ukewise known r,, on another
inclined plane whereon the gravity shall have the
value g^.
Here it is plain that the equation (1 bis) or (7),
which refers to the effects of the engine with inde-
finite load or velocity, will subsist if we introduce
into it successively M|, v,, and g^^ M^, t;, and g^^ in
place of the general values M, v and g. Conse-
quently there will result, for the solution of the
problem, the two conditional equations
«
By means then of these two equations, any two of
the dimensions of the engine may be determined,
and the other three assumed arbitrarily. We may,
for instance, previously choose, fix>m other con-
siderations, the pressure in the boiler, the diameter
of the cylinder, and the length of stroke of the pis-
ton, and determine the diameter of the wheel and
the vaporization fix>m the two conditions imposed.
OF THE PROPORTIONS OF THB ENGINES. 417
Then, introducing into the above equations, for the
given loads and velocities and the dimensions chosen,
their numerical values, those equations will contain
but two unknowB quantities, which will easily be
deduced from them by elimination.
Thus this problem would be as easy as the pre-
ceding one, and it would be the same with any other
combination of conditions that might be imposed to
determine the proportions of the engine. For this
reason we shall dwell no longer on these researches.
Sect. X. Of the special influence of each of the
dimensions of the engine on the effects produced.
It remains, in fine, as a general conclusion of the
preceding researches, to specify the peculiar in-
fluence of each of the dimensions of the engine on
the effects which are to be expected from it. This
inquiry will serve to establish fixed notions as to
the dimensions most favourable for the producing of
the divers effects that may be required of engines
about to be constructed.
1st. Examining equation (1 bis), namely,
1 2 jL ?
it will easily be recognised that the velocity of the
engine with a given load M, will be by so much the
greater, all things else being equal, as the vaporiza-
tion S is greater. Moreover, it will also be recog-
2e
418 CHAFTBB XIII.
nified that, for a given vaporization, the velodty will
be by so much the greater as the fector
D
has less value. It is in consequence to be con-
cluded that, in order to augment to the utmost
the velocity of an engine with a given load, we
must either employ a cylinder of the smallest
possible diameter, or make the wheel the largest
possible with reference to the stroke of the piston.
These consequences might however have been
seen d priori; for if we suppose a given vaporization
in the boiler, it is dear that the quantity of steam
which will result fix^m it per minute cannot issue
forth in the same time, by a cylinder of less
diameter, except on the condition of increasing
its velocity during its efflux, that is, of increasing
the velocity of the piston. As to the ratio between
the length of the stroke of the piston and the
diameter of the wheel of the engine, as it is known
that at every double stroke of the piston the engine
advances one turn of the wheel, it is readUy per-
ceived that the larger the wheel relatively to the
stroke of the piston, the greater must be the ve-
locity of the engine with a given load. This latter
circumstance shows also that in order to increase
the velocity of an engine, it is not absolutely neces-
sary to augment the diameter of the wheel ; for the
same end will be attained by diminishing the stroke
OF THE PROPORTIONS OF THB ENGINES. 419
of the piston. Thus, on railways of small width of
way, and on which in consequence it would not be
advisable to introduce wheels of too great a dia-
meter, a considerable velocity may be attained by
proportionally diminishing the stroke of the piston ;
but this disposition has the inconvenience of ren-
dering the velocity of the piston much greater for
the same velocity of the engine. For this reason,
when more velocity is desired, the better way is
' always to increase the vaporization ; which beyond
certain limits requires more width of way.
2nd. Referring to equation (2), which gives the
load the engine is capable of drawing at a desired
velocity, namely :
(l+»)(*±^) 15280 /+c > dU / J *±/
and making, in order to simpliiy, 9 = 0, that is,
supposing the train to be drawn upon a level, it
will be recognised that the load is by so much the
greater as the vaporization S of the engine, that is
the heating surface of the boiler, is greater; and
that, on the contrary, it is diminished by the values
of dy I and D, that is, by the dimensions of the
cylinder, the stroke of the piston, and the wheel,
which are proper to augment the velocity of the
engine.
Thus an increase of the heating surface of the
boiler tends to augment both the velocity and the
load of the engines, but a change in the diameter
of the cylinder, the length of the stroke and the
420 CHAPTER XIII.
diameter of the wheel, is favourable to the velocity
only at the expense of the load ; and if it be desired
that the engine should draw a considerable load at a
given velocity, it must have a large cylinder, a long
stroke of the piston, and a wheel of small diameter.
This circumstance explains itself easily, on consider-
ing first that the greater the diameter of the cylinder,
the greater is the effort exerted by a given pressure
of the steam. , As to the influence of the proportion
of the stroke of the piston to the diameter of the
wheel, it evidently results from this, that the power
of the steam acts at the extremity of the radius of
the crank of the axle, which is equal to the half
stroke of the piston, whereas the resistance of the
load acts at the extremity of the radius of the
wheel ; and it is well known that a force is by so
much the greater as it acts on a greater lever;
whence results that the longer the stroke of the
piston with reference to the wheel, the more ad-
vantage has the power over the resistance.
3rd. Examining the value of the useful effect
produced by the engine at a given velocity, namely,
from equation (3) :
and supposing, in order to simplify, ^r = 0, we find
that this useful effect is augmented, precisely by the
same causes as the load of the engine ; so that it
increases with the vaporization of the boiler, but on
i
OF THE PROPORTIONS OF THE ENGINES. 421
the contrary is diminished by the dimensions of the
cylinder, the stroke of the piston, and the wheel,
which tend to increase the velocity of the motion.
The divers e'xpressions of the useful effect neces-
sarily offer analogous variations, that is to say, the
dimensions which tend to augment the load will
have also the result of augmenting the effect of the
engine, in horse-power, the useful effect produced
per pound of fiiel and per cubic foot of water va-
porized, and they will diminish the quantity of coke
and water necessary to produce the effect of one
horse, or to draw a ton one mile.
4th. If we now seek what influence the propor-
tions of the engine will have on its divers effects,
the engine producing at the same time its maximum
useful effect, we first find that, since the velocity of
maximum useful effect is expressed by the equation
(4 bis), or
1 S D 1
V =
5280 d^ l + c n+qV
it is clear that this velocity will be augmented by
the vaporization of the boiler, as well as by those
values of d, I and D, which produce a similar effect
on the general velocity of the engine. Moreover,
it is reco^sed also that the greater the pressure in
the boiler, the less will be the velocity of the maxi-
mum useful effect of the engine ; which arises from
the circumstance that the steam is less in volume as
its pressure is greater.
422 CHAPTER XIII.
5th. Equation (5) , which gives the TnaTimnm load
of the engine,
"-(lV(V±,)D<--'-^'''' - IS? (ra*-"*'")-
shows that the maYimnin load of the engine is
totally independent of the vaporization in the
boiler, and that for given dimensions of the engine,
it increases precisely when the pressure P of the
steam in the boiler increases; and this effect is
owing to the atmospheric pressure then neutraliang
a firaction by so much the less of the effort applied
by the engine. As for the rest, the maYimimi load
is likewise, as in the general case, duninished by the
dimensions of the engine, which tend to increase
the velocity.
6th. Referring to the general conclusions deduced
from the examination of equation (3), which were
these, that all the dimensions proper to diminish
the velocity of the engine, have also the result of
augmenting its useful effect, it will be recognised
that, since the case of maximum useful effect is but
a particular case ot the general one, it must neces-
sarily be subject to the general conditions already
expressed. Consequently the maximum useful
effect of the engines will be augmented by the
same causes whidi increase the maximum load,
that is to say, by the increase of the pressure in
the boiler, by that of the diameter of the cylinder
or of the length of the stroke of the piston, and
OF THB PROPORTIONS OF THE ENGINES. 423
in fine, by the diminution of the diameter of the
wheel.
7th. Lastly, on examining equation (7), which
gives the vaporization of the engine, necessary to
draw a given load at a desired velocity, namely :
it is recognised that the vaporization increases with
the factor
that is to say, it is so much the greater as the
diameter of the cylinder and the length of the
stroke are greater, and that it is on the contrary
diminished by an increased diameter of the wheels
of the engine.
Sect. XI. Of the comparative effects of locomotive
engines upon the toide-gauge and narrow-gauge
railways.
We have just seen in the preceding paragraphs,
that the only means of really increasing the effects
of the engines consists in augmenting their vapor-
ization, that is, the heating surface of their boiler,
because this mode produces an increase of velocity
without prejudice to the load of which the engines
are capable. On the other hand, it is easy to con-
ceive tiiat on a railway of given width, the dimen-
424 CHAPTER XIII.
sions of the engines cannot be augmented inde-
finitely. It is necessary then to examine here how
the width of way may limit the size of the boilers,
and consequently the power of locomotives.
Almost all the railways of great traffic have been
hitherto laid down of the width of 4 feet 8^ inches,
which dimension was founded merely on custom.
In 1836, when the Great Western Railway was
made to form the communication between London
and Bristol, Mr. Brunei, jun., made the road 7 feet
in width. The question is now to examine what
advantages may result, with regard to the velocity
and the useful efiects of the engine, from this widen-
ing of the road.
It has been seen above that the locomotives em-
ployed on the Liverpool and Manchester Railway
vaporize on an avera^ 65 cubic feet of water per
hour, and this railway is 4 feet 8^ inches wide.
On the London and Birmingham, which is of the
same width, there are locomotives which vaporize
as much as 100 cubic feet of water per hour, and it
would be difficult to establish engines having a
greater vaporizing power on railways of this dimen-
sion, because the width pf the way would very
hardly admit of a farther augmentation of the
dimensions of the boiler. On railways then of
this width, locomotives of 65 cubic feet of vapor-
ization may be considered as engines of medium
force, and engines of 100 feet of vaporization, as
nearly the most powerful that it is possible to have.
OP THE PROPORTIONS OF THE ENGINES. 425
On the Great Western Railway, which is 7 feet in
width, the engines of medium force vaporize 'about
120 cubic feet of water per hour, and the most
powerful in use vaporize as much as 200 cubic
feet; but considering the interval which remains
between the boiler and the fieme-work of the
engine, there is room to think that, on this line,
engines might be established of 300 cubic feet of
vaporization, and even more, without very consider-
ably augmenting the weight of the engine.
K then, by means of the formulae developed in
the preceding chapter, we seek the velocity and
effects which these different species of engines are
capable of producing, we shall form the Table that
will be presented a little further on.
To perform this calculation, we proceed as was
done in Article III. of the preceding chapter, in
which the examples reported offer precisely the
results proper to the engines of medium force em-
ployed on the two widths of way under considera-
tion. Thus we adopt the dimensions of the engines
and the pressure of the steam admitted on each rail-
way ; we take the presumed friction of the engines at
15tts. per ton of their weight, as we have deduced
it from our own researches in Chapter VIII. Simi-
larly, from what experience "has proved, we take
the consumption of fuel per cubic foot of water
vaporized, at 9*2 fts. for engines of 65 cubic feet
of vaporization, at Sflbs. for those of 100 cubic
feet, and in fine, at 8"8Ibs. for engines of 120 cubic
426 CHAPTER XIII.
feet, 200 cubic feet and above, tbou^ it would
appeat tbat the consumption of these latter engines
ought to be less, because the size of the boiler is
always &yourable to the saving of fiid. To take
account of the variation of viq[X)rization mth the
velocity, we likewise adopt, according to experi-
ment, the vaporizations above indicated as those
which refer to the respective velocities of 20, 30,
25, and 35 miles per hour, for the different en-
gines, taking them in the order in which we have
placed them. We value the sur£BU» of the carriages
according to what has been indicated in the two
examples of Article HI. of the preceding chapter ;
and finally, we n^ect, for all the engines, the loss
of steam which may take place by the safety-valves,
because we suppose tfais loss corrected in all, or at
least in proportion to the total vaporization, and
that the divers effects produced will therefore, by
that cause, be all reduced in a proportional d^ree.
To establish the comparison of the different en-
gines on the most usual load, for the convey-
ance of passengers, we shall seek the velocity and
the consumption of coke of each engine with a train
of 50 tons gross, tender not included; and in the
last column we shall add the maximum velocity that
the engine is capable of acquiring, drawing its tender
alone and without any other load.
OF THB PROPORTIONS OF THE ENGINES. 427
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428 CHAPTER XIII.
Such are then the effects which are to be expected
firom these different kinds of locomotive engines ;
and the results which we have just signalized for the
engines of the London and Birmingham, and Great
Western Railways, will be found sufficiently con-
firmed by the experiments made in 1838, on those
two railways, at the request of the Directors of the
Great Western, when some difficulty arose respecting
the width of way.* Taking the mean of such of these
experiments as were made on trains of about 50 tons,
having regard to the average vaporization effected
during the trip, and adding an experiment recently
published by the Directors themselves of the Great
Western Railway, in which an engine, similar to
that of No. 11. of the preceding Table, drew a load
of 43 tons gross, tender not included, at the velocity
of 38 miles per hour, consuming 95 lb. of coke per
ton per mile, it will be recognised that the results
indicated by the calculation, for the locomotives
Nos. V. and VI., which have never been built, by
no means exceed the effects which may be expected
from those engines. As to the possibility of at-
taining velocities of 50 and 60 miles per hour, with
locomotives of sufficient vaporizing power, we deem
it completely proved by an experiment of our own,
made on the 3rd August, 1839, on the Great
Western Railway, with Mr. Daniel Gooch, one of
* Nicholas Wood's Report to the Directors of the Great
Western Railway.
OF THE PROPORTIONS OF THE ENGINES. 429
the Company's engineers. In this experiment, the
engine Evening Star, built by Mr. Robert Ste-
phenson of Newcastle, drawing only the tender
loaded with eight persons, repeatedly attained the
velocity of 55 '4 miles per hour ; and if the feeding-
pipes of the boiler had not been too small for that
velocity, an arrangement which has since been
altered, there is no doubt that we should easily have
maintained* that velocity throughout the trip, and
even have exceeded it ; but as those pipes could
not supply the expenditure of the boiler, the water
in the latter lowered rapidly, and having once at-
tained the velocity mentioned, we were obliged to
close the regulator and let the ^[igine run, without
working, to ^ve time for the boiler to fill again.
The results deduced from our formulae and con-
tained in the Table presented above, appear then
to us to be completely supported by the facts.
Thus it is manifest that locomotive engines on
wide-gauge railways can draw the * same average
load of 50 tons, or about 200 passengers, at much
greater velocities than the engines on narrow-gauge
railways, and that the velocity of the former may
even amount to double the velocity of the latter.
Such an advantage is certainly not to be neglected,
and it would be vain to object that the present
velocity is sufficient ; for that argument might have
been urged, either some years ago against the esta-
blishment of mail-coaches, or in our days against
any establishment of railways whatever.
J
430 CHAPTER xin.
It will be remarked, in the pre<iedii]g results, that
the surfdos velocity is purchased by a greater ex-
pense of fuel. This surplus of expense arises
undoubtedly in part from the excessive wei^t of
the engine and its tender, which together amount
to about 30 tons, instead of 15, which is the cor-
responding weight for engines on narrow-gauge
railways ; so that, for a load of 50 tons, the motive
power is affected with a weight of 30 tons in the one
case, and with a weight of but 15 tons in the other.
But that effect depends also especially on the
circumstance, that the resistance of the air, the
pressure in the blast-pipe, and the other passive
resistances, consume quantities of work by so much
the greater as the motion is performed with greater
velocity. It is then an inevitable result of the
velocity, whatever may be the width of way, and the
engine employed. To obtain conviction moreover
that the inconvenience of the greater weight of the
mover may be counterbalanced by opposite ad-
vantages, it suffices to compare the two species
of engines at the same velocity. Now, calculating
the load that a wide-gauge locomotive engine of
medium force, or of 120 cubic feet of vaporization,
can draw at a velocity of about 25 miles per hour,
we find, as may be seen in the example calculated
in Article III. of the preceding chapter, that that
load will be 147 tons, tender included, or 137
tons without the tender, and that the corresponding
consumption of fuel will be '30 ft. of coke per
OF THE PROPORTIONS OF THE ENGINES. 431
ton per mile. Comparing then this effect to that
of an engine of medium force of the narrow-gauge,
or of 65 cubic feet of vaporization, we have the
following results :
Velocity, in Load, in Coks» in
mQa per tans gnm, Itm* per
boaif tender not ton per
indnded. mile.
Engine of 65 cable feet of
vaporization, narrow-gauge .. 25*10 50 '47
Engine of 120 cubic feet of
vaporization* wide-gauge .... 25*55 137 *d0
Consequently, when a velocity of 25 miles per
hour is considered sufficient, it is ohvious that wide-
gauge locomotive engines have the advantage of
conveying much greater loads, and consuming less
fuel per ton.
We are then of opinion, that in countries where
as yet but few railways are made, it is worth con-
sidering whether, according to the circumstances, it
will not be advantageous to employ a greater width
of way than that in general use, and we must here
add that, for the most powerful engines of the above
Table, a way 6^ English feet in width appears to be
sufficient.
Sect. XII. Practical formuUB, to determine the
proportions of locomotive engines^ according to
given conditions.
Before terminating this chapter, we will here
give, in their numerical form, all the formulae which
we have just presented, to determine the proper-
432 CHAPTER XIII.
tioDS of the engines, according to given conditions.
For the signification of the signs employed, we refer
to Article III. Chapter XII.; and for the use and
complete intelligence of the formulae, we refer to
each of the respective sections of the present
chapter.
PRACTICAL FOEMOUB TO DETBRMINB THE FEOPOETION8 OF LOCO-
MOTIVE ENGINES, NECBSSAET TO FEODUCE GIVEN EFFECTS.
Total vaporizstion
of the boiler, in cii>
bic feet of water
per hoar.
w •••'''=?• 27^'7Cni- 1 - («±')*'^'~-~'- if J •• •
Square of the dia-
meter of the cy-
linder, in feet.
stroke of the piston,
in feet.
no) D-i!i iizi+p't,
Y7j--(6±y)M+^-«e«-_
IHameter of the
wheel, in feet.
(ll)...S- yij.^'.tr'(618 + P) Total vaporization
of the boiler, in cu-
«
bic feet of water
per hour.
(12)...P = (l + 8)J^[(6±^)M±^+w'2+ -L_] +2118+/>'r'
Total or absolute
pressure of the steam
in the boiler, in
pounds per square
foot.
• « •
OF THE PROPORTIONS OF THE ENGINES. 433
(13)...P*784^-.i-618 Total or absolute
pressure of the steam
in the boiler, in
pounds per square
foot.
(I4),..rf««784~. i._i-_ Square of the dia-
/ V 618 + P . ^ XV
meter of the cy-
linder, in feet.
(15).../=. 784^.?;.-~J — Stroke of the piston,
«' V 618 + P . ^ J.
m feet.
(16)...D«-L.rfa/.| (6i8^.p) Diameter of the
wheel, in feet.
(17) . . . rf8« (1 + a) -.^ ,— ii? .. Square of the dia-
^' P-21l8~^'r' ^^, ^ the cy.
Under, in feet.
i6±g)W±ffm + uv'' + -^
{18)..../=(U-8)£.. p ouB „V • S*«>1^«°^*«^ ?«*«"'
d^ P- 2118-^ 17 inieeL
/iftv r. ^f P-2118-/?'r' _. ^ . .
(19) . . . D== - — . s- • • • • Diameter of the
(6 +^)M'+mii + !•»'>+ ; — - wheel, in feet.
~ — 1 + 0
2f
CHAPTER XIV.
OF ADHESION.
In the two preceding chapters, we have given the
formulae for calculating the effects or the proportions
of the engines ; but we must now speak of another
condition without which the effects indicated could
not be produced. This condition consists in the
adhesion of the wheels to the rails being sufficient to
effect the motion of the load.
It has been observed, in the description of the
engine, that the effort of the steam being applied to
the wheel, the engine is precisely in the casef of a
carriage which is made to advance by pushing at the
spokes. Thus, as in this action the only fulcrum of
the mover is the adhesion of the whed to the rails,
if that adhesion were insufficient, the force of the
steam would indeed make the wheels turn; but
these, sliding on the rails instead of adhering to
them, would turn without advancing, and the
engine would remain on the same spot.
The heavier the train to be drawn, the more force
the engine must employ, and the more resistance
it must consequently meet with at the point on
which it strains to effect the motion. It might then
OF ADHESION. 435
be feared that with trains of considerable weight, the
engines would be unable to advance ; not that force
would be' wanting in the mover itself, but in the
fulcrum of the mover.
The experiments presented in Chapter XII. esta-
blish the measure of that adhesion in the fine
weather season. In all these experiments, not one
is found in which the motion was stopped or even
slackened for want of adhesion. And yet we find
among them loads amounting to above 300 tons.
If, for instance, we refer to the first experiment
made with the Fury on the 24th July, and take
account of the gravity in ascending the plane in-
clined ^, we shall find that the engine then drew a
load equivalent to 306 tons on a level. Since the
engine advanced with this load, it foUows that the
adhesion was sufficient. Now the weight of the
Fury is 8*20 tons, and that weight is so divided
that 5'5 tons bear on the hind-wheels, which are
the only propelling ones, the fore-wheels not serving
at all to urge the engine forward, but merely to
support it. It was then a weight of 5*5 tons that
drew 306 tons, or a weight 55 times as con-
siderable as itself; consequently, an engine having
its four wheels coupled, and thus adhering by its
whole weight, may draw a load equal to 55 times its
own mass.
We have said that the engine Fury adheres but
by two wheels. This disposition is general on the
Liverpool Railway for all the trip engines, because
436 CHAPTER XIV.
the adhesion of two wheels is sufficient for the
loads they have to draw. As to the engines which
serve as assistant engines on the inclined planes,
they work with the adhesion of their four or six
wheels, as has been said elsewhere. The engine
Atlas is the only one employed for the trips, which
differs from the others in this respect. This engine
has six wheels, four of which, of equal size, are set in
motion by the piston. The other two, smaller and
without flange, may be raised out of contact with
the rails by the action of the steam on a moveable
piston. This disposition, which prevents these
latter wheels from being inconvenient in turning, is
due to Mr. John Melling, sen., of Liverpool.
To Mr. Melling also is due another very ingenious
arrangement, by means of which an engine may be
made to adhere by all its wheels, notwithstanding
the difierence of their diameters. It consists of a
pulley, which is let down at pleasure between the
two pairs of contiguous wheels, and which connects
them so that one cannot turn without necessarily
drawing the other with it. By means of this ap-
paratus, engines may have their- wheels \inequal,
which is very advantageous to the good arrangement
of the machinery, and all their wheels need be put
in communication only at the moment when that
becomes necessary, which is done without stopping
the engine.
We have just expressed the adhesion, by giving
the measure of its effects ; *but that force itself may
I
OF ADHESION. 437
be expressed in a direct manner. The load of 306
tons produced a resistance, or required a tiPaction of
1836 lbs. ; the adhesion was then equal to at least
1836 lbs., otherwise the w^heel would have turned
without going forward. Now the adhering weight
was 5'5 tons, or, expressed in fts., was 12,320 lbs..;
it is plain then that the adhesive force was equal to
about ^ of the adhering weight. Considering that
every 6 lbs. of force corresponds to the traction of
1 ton on a level, this expression amounts to the
same as the first.
In winter, when the rails are greasy and dirty by
the effect of wet weather, the adhesion diminishes
considerably. However, unless in very extraor-
dinary circumstances, the engines are always ca-
pable of drawing a load of 15 waggons or 75 tons,
tender included, that is, 14 times their adhering
weight ; or, in other words, as the resistance of 75
tons is 450 lbs., the adhesive force is always at least
^ of the adhering weight.
Adhesion being indispensable to the creation of
the progressive motion, two conditions are requisite
for an engine to be capable of drawing a given load :
1st, the dimensions and proportions of the engine
and its boiler must enable it to produce, by means
of the steam, the necessary pressure on the piston,
which constitutes the force applied by the engine ;
and 2nd, the weight of the engine must be such as
to cause a sufficient adhesion to the rails. These
two conditions of force and weight should accord
438 CHAPTER XIV.
together ; for, were there a great force ci steam and
a slight SdhesioD, the latter would limit the effect of
the engine, and steam would be lost; and were
there too much adhesive weight for the powor of
the engine, that wei^t would, during the motion,
m
become a useless burdoi, since the limit of the load
would then be marked by the pressure of the
steam.
It is necessary therrfore, after having determined
the dimensions of the engines from the conditions
which they are to fulfil, as has been done in the
preceding chapter, to seek what ou^t to be their
weight so as to enable them to draw the greatest load
intended to be imposed on them during thdr work.
The enormous weight now given to locomotive
engines, generallj^ causes this condition to be ful*
filled of itself. Six- wheel engines however require,
in this respect, more attention than four-wheel
engines, because it often happens, on an uneven
railway, that a six-wheel engine is wholly suppcurted
on its four extreme wheels, whereas the middle
ones, which are the propelling wheels, being acci-
dentally situated immediately above a low part of
the railway, scarcely touch the rail, and therefore
have but a slight adhesion.
CHAPTER XV.
OF THE REGULATOR.
Sbct. I. Of the effects of the regulator on the
velocity of the engine.
It has been said, in the description of the different
parts of the engine, that the pipe which brings the
steam from the boiler to the cyUnders may be
closed, either entirely, or in part, by means of a
cock or regulator, and that the velocity of the
engine is regulated by this means. U becomes
necessary then to consider how this effect is pro-
duced, and how the formulae which we have given
may keep accoimt of it.
It is an opinion generally received, that by
opening or shutting the regulator more or less, the
pressure of the steam in the cylinder is augmented
or diminished. But we have proved that the pres-
sure in the cylinder is always strictly determined,
a priori, by the resistance of the load against the
piston. So long therefore as the load shall not
vary, the pressure in the cylinder will not vary, and
consequently the greater or less opening of the
regulator can make no difference in it. Besides,
440 CHAPTER XV.
how could the contraction of a passage change the
pressure of a gas or steam issuing through that
passage ? It may indeed change its quantity, be-
cause the smalhiess of the aperture prevents more
than a certain volume from passing in a given time ;
but unquestionably it can never change the pressure,
for it will always happen that as soon as the steam »
having got through the passage, shall arrive in the
cyUnder, and shall there acquire the pressure of the
resistance, the piston will recede without allowing it
to assume a higher pressure. And if it be supposed
that by enlarging the passage, the steam may be
made ta come ten or twenty times quicker, the
piston will recede ten times or twenty times quicker
also, since its motion is the result of the arrival of
the steam; but the pressure in the cylinder can
never exceed the resistance of the piston, because
the piston being nothing more nor less than a valve
to the cylinder, it would be supposing a boiler in
which the pressure of the steam should be greater
than that of the safety-valve.
Thus the narrowing of the regulator cannot
diminish the pressure of the steam in the cylinder.
Moreover, a diminution of pressure in the cylinder
would not account for the diminution of velocity of
the engine, which is observed when the regulator
is partially closed ; except indeed the motion should
be attributed, as it has been by some, to an excess
of the pressure of the steam in the cylinder above
the resistance of the piston. But this opinion
OF THK RBGULATOR. 441
would be altogether an error; for if such excess
existed, the motion of the engine would not be
uniform, but indefinitely accelerated. On the con-
trary, the pressure of the steam is equal to the
resistance of the piston, and the motion is owing to
the velocity with which the steam arrives, at that
pressure. Hence, the above-mentioned suppositions
are inadmissible. But the effects of the regulator
are easily accounted for in another manner.
The quantity of steam of a given density, which
issues forth through a determined orifice, being in
the ratio of the area of that orifice, it follows that if
we lessen the orifice of the regulator, we shall
thereby diminish the quantity of steam, at the
pressure of the boiler, which can issue by the orifice
of the regulator to pass into the cylinders. If how-
ever the fire be kept up at the same degree of
intensity, it will continue to produce the same
quantity of steam per minute. This steam, which
can no longer flow in totality towards the cylinder,
will therefore accumulate in the boiler, and there
rise to a still greater and greater density and elastic
force, till at last it be able to find some outlet.
Now the steam has two outlets whereby to escape
from the boiler, namely : the passage of the regu-
lator, which, notwithstanding its contraction, would
admit 4:^ the total efflux of the steam, as it is gene-
rated, if that steam acquired a sufficient degree of
density, or, in other words, a volume sufficiently
small for that efiect ; and the safety-valve, which
442 CHAPTER XV.
would equally admit of its escape, were the steam
to acquire a pressure sufficient to raise the valve.
Two cases then will occur, according as the steam,
continuing to accumulate in the hoiler, shall acquire
more promptly either the pressure which admits of
its issue by the safety-valve, or the density which
enables it to flow out entirely by. the regulator.
1st. If the r^ulator is much contracted, and if
the safety-valve of the boiler, on the contrary, is
fixed at a moderate pressure, the steam retained in
the boiler will soon attain the d^ree necessary to
raise the safety-valve. The valve then will be open,
and all the surplus steam generated in the boiler,
beyond what can issue by the regulator, will escape
into the atmosphere ; and this effect will continue
so long as nothing shall be changed in the engine,
because there will still be the same necessity for
the steam to effect its efflux as it is generated, and
because the resistance of the obstacles which it has
to overcome will remain still the same.
Thus, the effect of the contraction of the regulator
will be, to cause a portion more or less of the steam
produced by the boiler to be lost in the atmosphere ;
and as the effects of the engine are attributable only
to the effective vaporization, that is to say, to the
portion of the total steam which really penetrates
into the cylinders, it follows that the velocity of the
engine will be reduced precisely in proportion to
the quantity of steam lost. Hence, the effect of
the contraction of the regulator will be to reduce
OF THE REGULATOR. 443
\
the velocity of the engine immediately. Then, after
the first few moments of the contraction of the re-
gulator, the. engineer seeing a considerable quantity
of steam running to waste by the safety-valve, will
naturally cease to keep up his fire with the same
activity. The vaporization produced in the boiler
will be diminished in consequence; and by con-
tinual reduction of the fire there will at last be no
more steam generated than may efiectively pene-
trate into the cylinders. From this moment then
the blowing of the safety-valve will cease, and the
velocity of the engine will continue as it was regu-
lated at first by the contraction of the regulator.
Consequently it is manifest that the regulator
diminishes the velocity of the engine, by imme-
diately reducing the effective vaporization, and ul-
teriorly the total vaporization of the boiler ; and it
is also manifest that its effect is not to diminish the
pressure in the cylinder, but to augment the pres-
sure in the boiler.
2nd. We have just supposed the case wherein the
regulator is sufficiently contracted to make the
safety-valve blow, and have seen what effects will
result therefrom. But another case may occur,
namely : that in which the regulator should also be
contracted, but yet not sufficiently so to make the
safety-valve blow ; that is to say, the case wherein
the steam, accumulating in the boiler, should attain
the density which permits its total efflux by the
regulator, before it attains the pressure necessary
to raise the safety-valve. Then, since the valve
444 CHAPTBB XV.
does not blow, and no portion of the steam pro-
duced is lost, it is clear that all the steam will pass
into the cylinder and act there as before. Hence the
velocity of the engine will in nowise be changed ;
for that velocity cannot be augmented nor dimin-
ished except by an increase or a reduction of the
effective vaporization of the engine, and this cir-
cumstance does not occur in the case supposed.-
Notwithstanding, therefore, the contraction of the
regulator, the velocity of the engine will remain the
same, and there will result, as in the preceding case,
only an increase of pressure in the boiler.
From these considerations, we see that the unique
and immediate effect of the contraction of the regu-
lator is to augment the pressure of the steam in the
boiler ; and that if the increase of pressure is such
as to cause a loss of steam by the safety-valve, the
velocity of the engine will be reduced precisely in
the same proportion, but that if no such loss takes
place, the velocity undergoes no reduction.
Now, in the formulae which we have given to
calculate the velocity of the engines, the quantity S
represents the effective vaporization of the engine,
that is to say, the quantity of water which, being
converted to steam, really penetrates into the cylin-
ders and acts upon the piston. If, notwithstanding
the contraction of the regulator, there is no loss of
steam by the safety-valve, the effective vaporization
of the engine will not be changed, that is, the
quantity S will remain the same, and consequently
the formulae will still continue to give the same
OF THE REGULATOR. 445
result for the velocity of the engine. On the other
hand, if a loss of steam takes place by the safety-
valve, that loss must obviously be subtracted from
the total vaporization of the boiler, in order to
deduce from it the effective vaporization, or the
quantity which ought to be substituted for S in the
equations, and then the result of those formulae will
be reduced in a proportionate quantity. In either
case, therefore, the formulae which we have given
will always continue to make known the true effects
produced by the engine. All they require is, that
account be taken of the loss by the valves, when
that loss occurs, and we have already shown in
Chapter X. how it may be estimated.
These considerations will be found confirmed by
the experiments presented in Chapter XII. It will
there be observed that the formulae give results
quite as exact for the case wherein the regulator was
partially closed, as for the case in which it was
entirely open. And the reason is this, that when
the partial close of the regulator was attended with
a loss by the- valve, we took account of it in the
value of the effective vaporization S, by taking that
value equal to the total vaporization of the engine,
diminished by the. loss at the valves.
Sect. II. Dimensions of the steam-passages in some
locomotive engines.
We will close this chapter by giving the diameter
of the steam-pipes in the engines which we sub-
mitted to experiment, and in some others whose
446
CHAPTER XV.
dimensions have been given at the beginning of this
work. The pipes here considered are those which
lead separately from the boiler to each slide-box.
Those which afterwards lead from that box to the
cylinders, are of a corresponding surface, though of a
different shape. For instance, when they form the
continuation of a tube 3 inches in diameter, they are
made 7 inches long by 1 inch wide, which presents
the same surface for the passage of the steam.
It will be remarked that the steam-passages are
much wider in locomotive engines than in stationary
steam engines, since in these the area of the steam-
passage is but ^ of the area of the cylinder, while
in locomotive engines the proportion between the
same parts is in general i^ .
Steam-pipes in some of the locomotive engines of the lAoer-
pool and Manchester Railway,
Name of the
Diame-
terofthe
Stroke
of the
Heating sur&ce
Inner dia-
meter of
the steam-
of the
of the
engine.
cylinder.
piston.
fire-box.
tubes.
pipes.
inches.
inches.
sq. feet.
sq. feet
inches.
Samson.
14
16
40-20
377-41
3-25
Goliath I.
14
16
40-31
355-84
3-25
Atlas.
12
16
5706
197-26
3-25
Vulcan.
11
16
34-45
267-84
3-50
Fury.
11
16
32-87
267-84
3-50
Vbbta.
IH
16
4600
215-66
3-25
Lexdb.
11
16
34-57
267-84
3-50
FiRBFLT I.
11
18
43-91
317-71
300
Star.
14
12
49-71
279-18
3-75
CHAPTER XVI.
OF THE LEAD OF THE SLIDE.
Sect. I. Of the nature and effects of the lead of the
slide.
Wb have said, in describing the different parte of
the engine, that it is the^lide which successively
opens and shute the steam-ports above and below
the piston, so as to apply the effort of the steam
alternately on each side. Were the engine regulated
as it might seem natural to regulate it, the slide
would keep the steam-port open till the piston
arrived at the bottom of the cylinder. At this
moment it would change: the first passage would
be closed, and the opposite one opened. Then the
motion of the slide would exactly accompany that of
the piston, that is to say, their alternations would be
strictly simultaneous.
But the thing is not so ordered. At the moment
when the piston is about to terminate ite stroke, it
is needless and even detrimental to the engine to
apply any new impulsion on it, since it is then* at
the moment of stopping, to perform ite retrograde
stroke. Besides, it is proper to allow the steam,
448 CHAPTBR XVI.
which now fills the cylinder, time to escape as much
as possible, before the piston is brought back in a
contrary direction, since it would otherwise con-
tribute to form an obstacle, on account of the small-
ness of the orifice of the blast-pipe ; and finally,
rather than let the piston strike against the end of
the cylinder, or exert at least an effort in that
direction against the crank of the axle, it is prefer-
able to present to it an elastic body which may
deaden its shock. With this threefold purpose,
then, the motion of the slide is regulated in such
sort, that successively, and before the piston reaches
the end of the cylinder^ the three following opera-
tions are performed: 1st, the communication is
intercepted between the boiler and the steam-port
through which the steam is actually coming, which
suspends all addition to the motive force ; 2dly, the
communication of the same port with the waste
steam-port is opened, which permits the escape of
the steam by anticipation, while it still continues
its action ; 3rdly, the communication between
the boiler and the steam-port which conducts the
steam upon the piston, in a contrary way to its
motion, is opened ; which deadens the shock of the
piston, reKeves the joints of the machinery, and
enables the steam to act with full force on the
piston, as soon as the latter begins its retrograde
stroke. These three successive operations, as we
have said, are performed before the piston reaches
the bottom of the cylinder, and, by means of divers
OF THE LEAD OF THE SLIDE. 449
dispositions, they may be so regulated as to take
place on points more or less anterior to the end of
the stroke.
When the engine is regulated as we have just
explained, it is visible that at the moment when the
piston terminates its stroke to begin another, the
slide has already, for a certain space of time, been
intercepting the coming of the steam in favour of
the motion, and has even already admitted it in the
contrary direction during another interval of time
less than the former ; or, in other words, the slide
has already traversed a certain space in the di-
rection of its stroke, from the moment when it
closed the first passage, and another space less than
the former, from the moment when it opened the
contrary passage. It is this anticipation of the
motion of the slide upon that of the piston which is
called the lead of the slide^ because it indicates by
how much the motion of the slide precedes that of
the piston; but it is conceivable, from what has
been said, that a distinction is to be made between
the lead of the glide for the suppression of the steam,
and the lead of the slide for the admission of the
steam, though the latter is more particularly under-
stood when it is simply said the lead of the slide.
These two sorts of lead are sometimes distinguished
by saying the lead on the exhausting side and the
lead on the boiler side, but the former mode appears
to us to be more exact.
When the slide valve is single, that is to say, con-
2g
450 CHAPTER XVI.
sisting of a single box, like that of fig. 26 (PI. IV.) »
the difference between the two leads is equal to
twice the overlap of the slide. In effect, on ex-
amining that figure, which represents the slide at the
moment when it changes the passages of the steam,
and supposing its motion to have been in the direc-
tion of the arrow, it will be recognised that as soon
as the slide arrives at the position a, the coming of
the steam is intercepted in the left-hand passage,
but that the right-hand passage does not begin to
open till the sUde attains the position c. If then we
suppose the passage still more opened, and the
slide arrived at the position d at the same time that
the piston reaches the bottom of the cylinder, it is
plain that the quantity cd hy which the passage is
then open, will be what we call the lead of the slide
for the admission of the steam ; but that the oppo-
site passage will have been shut, and consequently
the motive force, in the direction of the motion,
will have been intercepted from the point a, that is
to say, the lead for the suppression of the steam will
necessarily be equal to the lead of admission aug-
mented by twice the overlap of the sUde. When
the sUde is double, or composed of two boxes which
may be set further apart or nearer to each other at
pleasure by means of an adjusting ' screw, each lead
may be regulated separately at the point which may
be judged suitable, and this is an advantage, but the
slide is more liable to get out of order.
As the disposition of the slide; which has just
been described, has the result of suppressing the
OF THE LEAD OF THE SLIDE. 451
motive force, at a certain point of the stroke of the
piston, to introduce it afterwards in the contrary
direction, it is evident that its effect on the engine
cannot be calculated till after an exact determination
of that point of the cylinder, at which the piston is
at the moment when the close and the opening of
the respective passages take place. This is there-
fore the first inquiry that wiU occupy our attention.
With this view, we return to the single slide
valve represented in figs. 10 and 26. On ex-
amining these two figures, it will be perceived that
if the radius of the eccentric were strictly at right
angles with the radius of the crank, it would then
so happen that the sUde would be in its middle
position, indicated by the figure, precisely at the
moment when the piston should arrive at the end
of its stroke. In this case, the suppression of the
steam in favour of the motion would take place, be-
fore this point, by a distance equal to the overlap
of the slide on the two ports ; and the admission of
the steam by the opposite passage would take place,
after that same point, by a distance equal to the
same overlap. But if it be wished to give the
engine a certain lead of the slide for the admission
of the steam, the passage of the steam opposed to
the present motion of the piston must be already
open a certain quantity, at the moment when the
piston terminates its stroke. To this end, therefore,
the radius of the eccentric must incline forward,
from the perpendicular to the radius of the crank,
452 CHAPTER XVf.
in an angle corresponding to the lead in question
augmented by the overlap of the slide. In effect, if
it be thus, we see that when the radius of the crank
coincides with the horizontal line, that is to say,
when the piston is at the end of its stroke, the
radius of the eccentric has passed the vertical by a
quantity corresponding to the lead of admission plus
the overlap ; that is to say, the slide has passed its
middle position, just the quantity necessary to open
the steam-port the quantity indicated by the lead.
This premised, suppose 6 D' (fig. 27) to represent
the radiiDS of the crank, and hb' the radius of the
eccentric. When the radius of the eccentric co-
incides with the vertical, the slide is in its middle
position and all the passages are closed. After it
has passed this point a quantity equal to the over-
lap, the passage of the steam opposed to the motion
of the piston will begin to open, and when the radius
of the eccentric shall have reached fteT, the slide will
open that passage the quantity indicated by the
lead. But since the eccentric and the crank turn
in one piece with the axle of the engine, it follows
that their radii describe equal angles in the same
time. Hence, while the radius of the eccentric
describes the angle ft'ftcT, the radius of the crank
describes an angle D'6B equal to. the former. On
the other hand, while the eccentric describes the
angle Vhd\ the slide, which moves horizontally,
traverses the space 6rf, which is equal to d!p ; that
is to say, it traverses the sine of the angle Vb^^ in
OF THE LEAD OF THE SLIDE. 453
a circle whose radius is equal to that of the eccen-
tric. Similarly, while the crank describes the angle
D'6B, the piston traverses the space DB, that is,
the versed sine of the angle described, in a circle
whose radius is equal to that of the crank.
Finally therefore, while the slide, departing from
its middle position, performs the sines of the angles,
in the circle of the eccentric, the piston, to finish its
stroke, performs the versed sines of the same angles,
in the bircle of the crank. Consequently it will
be easy to find the correlative situations of those
two pieces. It wiD suffice for this purpose, in prac-
tice, to draw exactly and by the scale the figure 27,
in which bs is the radius of the eccentric or the half
range of the slide, &B the radius of the crank or the
half stroke of the piston, and db the distance at
which the sUde is supposed to be from its middle
position. Then, raising at the point c2, the perpen-
dicular dcty we have the point df ; afterwards taking
the angle B6iy equal to the angle b'bd\ we deter-
mine the point D", and finaUy, letting fall the per-
pendicular DD, we have definitively the distance
DB, between the point D, where the piston then is,
and the point B which is the end of its stroke.
If it be desired to find the quantity DB by calcu-
lation, it will suffice, from what has just been said,
to consider the given distance db as the sine of an
angle, and to seek the corresponding versed sine.
Therefore, the ratio of the line db, to the radius bs,
454 CHAPTER XYI.
of the circle in which that line is drawn, must be
found; which is easy, since those two lines are
known. Then the logarithm of that ratio must be
taken, and that logarithm sought in the column of
sines of a Table of ordinary sines. Close to this will
be found the logarithm of the corresponding cosine,
and consequently on seeking the number which that
logarithm represents, the cosine of the angle de-
scribed will be known. Subtracting this cosine
firom unity, the difference will be the versed sine of
ihe same angle. This will then be the ratio between
the line DB and the radius &B of the circle in which
that line is drawn. Consequently, as the line &B is
known, it will be easy to determine from it the ab-
solute measure of DB the line sought.
If we take for example an engine in which the
stroke of the piston is 16 inches, range of the slide
3 inches, overlap of the slide over the steam-ways
^ inch ; and if we suppose the engine to have a lead
of admission of f inch, and a lead of suppression of
i inch ; and it be required to find at what distance
from the end of the cylinder the piston is when the
steam is intercepted, and at what point it is when
the steam is introduced against it, we shall find by
following the calculation indicated above, and ap-
plying it successively to the two given distances,
that the space remaining for the piston to traverse
at the moment the steam is intercepted in favour of
the motion, is 1*50 inch ; and that when the steam
OF THB LEAD OF THE SLIDE. 455
is introduced in the opposite direction, the piston is
'73 inch from the end of its stroke. The figure 27,
constructed by the scale, gives the same result.
If we suppose in the same engine a lead of i and
f inch in each respective direction, we find by a
similar calculation, that the space remaining for the
piston to traverse when the arrival of the steam is
inteircepted in the direction of the motion, is '25
inch, and that the steam is introduced in the oppo-
site direction when the piston is '03 inch from the
end of its stroke.
These examples show how, when the lead is
given, or when the situation of the slide is known at
any moment whatever, the point at which the pis-
ton is at the same moment may always be deduced
fr6m it.
Sect, II. Of the effects of the lead of the slide on
the velocity of the engine.
We have already mentioned the advantages arising
from the lead of the slide, with regard to the play
and the conservation of the engine ; but there is
another advantage no less important, resulting from
this disposition, namely, that of obtaining a greater
velocity, and consequently a greater useful effect
of the engine with a given load.
This effect is easy to comprehend ; for if the sup-
pression of the steam from the boiler, instead of
being made precisely at the end of the stroke of the
456 CHAPTER XVI.
piston, takes place, for instance, at the moment
when the piston is yet an inch from the bottom
of the cylinder, from that moment steam ceases to
flow into the cylinder. Thus, with r^ard to the
quantity of steam admitted into the cylinder or
expended at each stroke of the piston, the length
of the stroke is really diminished an inch. Now it
is the quantity of steam produced by -the boiler
which regulates and limits the velocity of the engine.
Suppose that such production frumished m cylinders-
full of steam per minute, when the total length I of
the stroke was filled with steam : now no more than
the length I— a is filled with steam; the same produc-
tion then will fill per minute a number of cylinders
expressed by wi X Hence, in fine, the velo-
city of the engine will be increased in the inverse
ratio of the lengths of the cylinder which are filled
with steam.
It is to be observed, indeed, that while a lead is
given to the slide, to suppress the steam coming
fix)m the boiler, a lead is also given to admit the
steam against the piston, before the latter has
reached the bottom of the cylinder. There results
then an increase in the mean resistance opposed to
the motion of the piston during the whole of the
stroke ; and since the velocity of the engine de-
creases as the resistance which it has to overcome
becomes greater, it might be deemed that this cir-
cumstance compensates for the former. But as, by
OF THE LEAD OF THE SLIDE. 457
means of double slide valve boxes, it is possible
to have a considerable lead for the suppression of
the steam, and a very small one for the admission of
the steam in the contrary direction, and as, even
with single slide valves, the steam is never ad-
mitted against the piston but when the latter is at
a very small distance from the end of the stroke,
and consequently at a point where a great force
could produce but a very small effort against the
motion of the crank of the axle, it will be recognised
that this circumstance will not sensibly retard the
progress of the engine. It may then be ^generally
admitted that the velocity of the engine will increase
in the ratio of the total stroke of the piston, to the
portion traversed at the moment of the suppression
of the steam by the effect of the slide.
This premised, it is visible, from the calculation
which we have given in the preceding section, that
when the lead of the slide for the suppression of the
steam is but f inch, on a total range of 3* inches,
the increase of the velocity of the engine must be
inconsiderable, since the steam is then suppressed
on '25 inch only, or on ^ of the total stroke of the
piston. If the lead of suppression amount to f or
f inch, it produces a more sensible effect, which
nevertheless may easily be compensated by the
strength of the wind, by care in maintaining the
fire, or by the quality of the fuel ; but if it amount
to i inch, calculation shows that it may produce
an augmentation of about two miles on a velocity
458 CHAFTSR XVI.
of thirty mfles per hour ; and in this case as weD
as in those in which the lead is greater still, it is
concetvable that its effects must mviifest themselyes
in practice.
Among all the engines employed in the experi-
ments presented in Chapter XII., there was not one,
except the Vbsta ^vrtiich we shall presently notice,
in which the lead of the slide was in the case last
m^itioned, that is, in which the lead of the slide
could have any very sensible effect on the velocity.
It is besides to be observed that when, in Chapta
X., we determined the effectioe -vaporization of the
engines, or the loss of water carried with the
steam in a liquid state, we did, in fact, take
account of the lead of the slide for each engine.
In effect, since the engine had then a lead of the
slide, we ought to have calculated the cylinder-
full, not by the entire stroke of the piston as we did,
but by the stroke after deducting the portion cor-
responding to the slide ; that is to say, retaining the
notations just employed above, by the length I — a.
But then the velocity of the engine, corresponding
to the real vaporization of all the water consumed
by the boiler, would have been increased in the ratio
' ; and in consequence the effective vaporiza-
I '^ a.
tion would have been diminished in the ratio — - — •
The calculation performed with this new effective
vaporization, would then have given for the engine
OP THB LEAD OF THE SLIDE. 459
a velocity less in the same ratio ; and in fine, to
take account of the lead of the slide, it would have
been necessary to multiply that velocity by the ratio
— - — • Hence we should thus have fallen back on
the same velocity which we obtained more simply
by the method followed ; and for this reason, con*
sidering besides how small the lead was, in the
engines submitted to experiment, we preferred not
to let those details figure in the calculation.
In the experiments of Chapter XII., and in all
the calculations of velocity made from our deter-
minations, on engines having but little lead of the
slide, it becomes needless then to enter into the con-
sideration of the lead. But the engine Vesta, as we
have said above, forms an exception in this respect.
In effect, there existed in that engine a peculiar
disposition which admitted of changing the lead of
the slide at pleasure ; and while the engine was
ascending the inclined plane of Whiston^ which was
the moment when its efiective vaporization was cal-
culated, the lead of the slide for the suppression of
the steam had been reduced to f inch, whereas during
the rest of the trip that lead had been fixed at ^
inch. The eff^ective vaporization of the engine is then
determined as comprehending a lead of only f inch
instead of ^ inch ; and as the former of these two
leads reduces the stroke of the piston 1*50 inch,
while the latter reduces it 3*35 inches, it becomes
necessary, in order to take account of this difference,
460 CHAPTKR XVI.
to calculate the velocities of that engioe by taking
the effective stroke of the piston at 12*65 inches,
instead of 14*50 inches, as it was ¥rith the lead of f
inch. This we did in calculating the velocities of
that engine, and had we not had regard to this cir-
cumstance, the calculation would have given about
3 miles less on each of the velocities of the engine.
From what has just been seen, the lead of the
slide augments the velocity of the engine with a
given load, and consequently its useful effect with
that load Therefore, as the lead of the sUde shall
be augmented, the useful effect will augm^it at the
same time, and this augmentation will continue till,
by reason of the lead, the effective stroke of the pis-
ton is so much reduced, that the given load becomes
a mcucimum load for the engine with that stroke.
Beckoning from this point, the lead of the slide, and
consequently the useful effect of the engine with the
given load, admit of no further augmentation, since
any further increase of the lead, or, in other words,
any further diminution of the effective stroke of the
piston, would render the engine incapable of draw-
ing the desired load.
Sect. III. Of the effects of the lead of the slide on
the maximum load of which the engine is capable. .
The advantages of the lead of the slide, which we
have just noticed, are very important, since they
consist in augmenting the velocity of the engine
OF THE LEAD OF THE SLIDE. 461
with a given load, or, in other words, its useful
effect for a given vaporization, which impUes the di.
minishing of its consumption of fuel for determined
effects. These advantages are produced in the in-
verse proportion of the lengths of the cylinder
which are filled with steam at each stroke of the
piston, and are therefore perfectly analogous to
those which would result in the engine from an
actual diminution of the stroke of the piston.
But they are attended with a disadvantage which it
is necessary to notice here, and which would equally
occur in the case of an actual diminution of the
stroke of the piston. The disadvantage consists in
this, that the maximum load which the engine is
capable of drawing becomes less at the same time ;
so that, for the producing of certain effects, it may
be advantageous to diminish, or even altogether to
suppress, the lead of the slide.
To be convinced of this fact, it suffices to observe
that at the moment when the piston reaches the
point which corresponds to the lead of the slide for
the suppression of the steam, the motive force is
suppressed ; and that, when the piston, continuing
its stroke in virtue of its acquired velocity, arrives
at the point which corresponds to the lead for the
admission of the steam, it not only receives no fur-
ther impulse in the direction of the motion, but
suffers an opposition from the motive force itself,
then let in against it. Now the piston cannot stop ;
it must finish its stroke. It is therefore obliged to
462 CHAPTER XVI.
drive back the new steam which obstracts its way ;
and as it consumes in overcoming the obstacle a
quantity of work equal to that which this steam
would have communicated to it, it follows that
through the space yet remaining to traverse, there
is destruction of the force previously acquired on an
equal length of the cylinder. Thus, representing by
a and fi the two portions of the stroke of the piston,
which correspond to the two leads for the suppres-
sion and admission of the steam, we see that the
effect of the motive force, for the definitive motion,
is now produced only on the length of the stroke,
diminished first by a and afterwards by /8, or that
there really remains, for the effort exerted by the
engine, a stroke equal only to Z — « — )8.
It will be remarked, indeed, that at the moment
the steam is intercepted and the waste steam-port
open, the motive force of the motion is not sup-
pressed instantaneously, and that on the opening of
the opposite port, the motive force is not let in
instantaneously in the opposite direction ; for, as the
steam requires a certain material time, either to
escape firom above the piston, or to penetrate on the
opposite side of it, it follows that during its efiiux
by the blast-pipe, that steam does not entirely cease
to exert an effort on the piston; neither, during its
admission against the motion of the piston, has it,
from the first, all the pressure of which it is capable
to resist it. Moreover, during this suppression of the
motive force in one direction and its introduction in
OF THE LBAD OP THE SLIDE. 463
the other, it will be remarked that the piston is very
near the end of the cylinder, which occasions its
action on the crank, that is, its action to produce or
retard the motion of the engine, to be nearly null.
From these two circumstances then it results, that
the loss of motive force on the length a of the stroke
of the piston, and its introduction in the opposite
direction on the length fi of the same stroke, are but
partial ; but calculating approximativdy, the effects
of the engine may nevertheless be computed in
supposing the effective stroke i^educed to the length
Now, referring to the expression of the maximum
load that the engine can draw (Chap. XII. Art. II.
Sect. II.), we recognise that the more the quantity I
diminishes, that is, the shorter the stroke of the
piston becomes, the more the corresponding value
of the load diminishes. Moreover, while the motive
force is exerted only on the length Z— «— )8, the
resistance of the load continues nevertheless to be
exerted on the total length I of the stroke. From
this fact then results a new disadvantage to the
power, that is to say, a new diminution of the
maximum load; and consequently, by these two
causes, the extreme load of which the engine is
capable wiU be by so much the less as the lead of
the sUde is greater.
To recognise by direct experiment to what degree
the maximum load of an engine may be diminished
by the lead of the slide, we undertook a series of
experiments on the subject with the engine Vesta.
464
CHAPTER XVI.
By a peculiar disposition, due to Mr. J. Gray, one
of the engine-builders of the Liverpool and Man-
chester Railway Company, this engine could, without
interrupting its progress, be regulated for different
leads of the slide, so that, with the same load and
on the same ground, the effect of those different
changes might be tried. They were produced by
means of three notches, more or less advanced on
the eccentric, and on which the driver might be
brought at pleasure by means of a lever. The total
range of the slide was 3*38 inches, and the three
notches gave the following leads of the slide :
1st notch
2nd notch
drd notch
r lead of suppression
\ lead of adinission
r lead of suppression
\ lead of admission
r lead of suppression
\ lead of admission
4 inch.
t
T
V
5
T
To render the differences more sensible, it was
between the first and the third of these positions of
the slide that we endeavoured to obtain a com-
parison. Consequently, on the 16th August, 1834,
in the morning, and on the same day in the evening,
the engine having been brought to the foot of the
incUned plane of WhistoUy inclined ^, first with a
train of 20 waggons, and afterwards with a train of
8 waggons, every one of which had been previously
weighed, a number more or less of these waggons
was detached successively, and with each of these
loads the greater and the lesser lead were succes-
sively tried. The results of these trials are pre-
sented in the following Table.
OF THB LEAD OF THE SLIDE.
465
8
■S
«1
•s
1
I
I
I
lit
•A
t4
W9 lO
■ •
I
•ON
1
>
I
11 ^
11
s
"S
1
s. s.
5
•a
a
1 1
I
S
OO 09
QD
Hi
•g.
s.
s
5
QD CO
00 Oi
^ eo
U3
lid
•a
fill
CO 02 09 O
lA QD lO *A
p CO il» O
Ok ^ CO c«
CO CO CO CO
»J a K £;^ > p
•M to
M
•I
I i i
<^ ? s ?
iO 00 (-^ eo
I
'B
«• d
S "8
1 1 1 f 1 1
1 1:1 I
g
^
2h
466 CHAPTER XVI.
From these experiments it appears, that all the
eDgine could do, with the leads of ^ and |- inch,
was to draw a load weighing 32*05 tons ; and that
with the leads of f and ^ inch it could, with the
same pressure in tlie hoiler, draw a load of 39*05
tons. Taking into the account the gravity of the
train and engine on the plane inclined ^, these two
loads are equivalent to 212 and 248 tons on a level.
Thus the maximum load of the engine was reduced,
by the lead, about ^, which may become important
under certain circumstances.
Sect. IV. Of the manner of regulating the lead of
the slide.
The preceding researches make known the effects
of the lead of the slide, either on the velocity, or on
the maximum load of the engine. We are then to
be guided in this respect by the effects that are
desired to be obtained from the engine.
It is besides an easy thing to know the lead of
the slide, and to regulate it at the point that may be
thought proper.
After having opened the door of the smoke-box
situated under the chimney, and taken off the top
of the slide valve box, so as to uncover the slides
and observe their motion, the engine must be gently
pushed forward on the rails, by hand, till the crank
of the axle lies perfectly horizontal.
At this moment the piston is at the end of the
OF THE LBAD OF THE SLIDE. 467
cylinder. Measuring then the quantity by which
the slide now opens the steam-port/ we have the
lead of the slide.
If it be desired to diange the lead, the crank
must be retained in the same position, and detaching
the driver which is fixed to the axle only by a stop
screw, the eccentric must be turned by hand till
the slide, which moves at the same time, shall have
opened the steam-port the desired quantity. Then
the driver is to be refixed so as to hold the eccentric
in that position. This operation being ended, it is
plain that every time the crank shall Ue horizontally
or the piston be ready to begin its stroke, the slide
will be found to open the steam-port the proper
quantity.
We have said, that to bring the crank horizontal,
it is in the forward direction that the engine must
be pushed. The motive of this distinction is, that
all the joints be tightened in the same manner as
they are in the progressive motion of the engine.
It is necessary also to bear in mind that these joints
will be still more tightened, and the lead of the
slide somewhat reduced, when the engine has to
sustain the tension produced by a considerable
load.
Another attention is necessary before giving the
lead, or measuring it, and this is to ascertain that
the slide has an equal play between the three ports
of the cylinder; that is to say, that in its two
extreme positions it is equally distant from the two
468 CHAPTER XVI.
sides of the middle or wagte steam-port. Otherwise
the lead of the slide would not be equal in the two
motions of the piston. This defect, if it exist, is
easily corrected by loigthening or shortening the
eccentric rod as may be required. This rod is pur-
posely formed of two parts (figs. 9 and 10), ter-
minated by a rig^t and left screw, and joined by an
adjusting4x>x E. When the box is turned, for
instance, to the rig^t, the two screws tighten and
the rod shortens. If on the contrary it is turned to
the left, the two 8cre¥r8 become less ti^t and the rod
lengthens.
The r^ulation of the slide then is an easy ope-
ration.
The lead of the slide may, moreover, be changed
with tolerable exactitude without opening the engine.
It suffices to make beforehand on the axle, with a
chisel and a hammer, two or three notches corre-
sponding to two or three positions of the driver for
given leads. These marks being once carefully de-
termined as above, it is easy, by advancing the
driver from one to the other, to make the slide pass
from one lead to another greater or less. This is
the means which we employed in some essays which
we first made on this subject with the engine Leeds,
and in which we successively changed the lead,
from nil to ^ and f inch.
The engine-men have several approximative ways
of attaining the same end. They have remarked
that, in general, a variation of ^ inch for the driver
OF THE LEAD OF THE SLIDE. 469
•
in the opeDing of the eccentric, corresponds to a
variation of \ inch in the lead of the slide. Thus,
knowing the actual lead of the engine, they may,
guided by this observation, diminish or augment
that lead as much as they think proper. They
attain their end also by loosening some keys or
joints, so that the eccentric-rod no longer draws the
rod of the slides immediately after it, but leaves, for
instance, \ inch of play in the communication of
the motion from the one to the other. It is readily
conceived that, by this means, the slide will begin its
motion ^ inch after the eccentric. If then the slide
had before a lead of f inch, its lead afterwards will
be but f inch. But this means and other similar
ones are detrimental to the engine.
CHAPTER XVII.
OF INCUNED PLANES.
Sect. I. Of the load on a level, which corresponds
to the load on a given inclined plane, and vice
versd.
We have already shown, in Chapter VI., the means
of computing the resistance opposed to the motion
of the engines, by the gravity of the trains placed
on incUned planes; but as many other questions
occur relative to inclined planes on railways, we
must here return to the subject, to solve the pro-
blems which arise out of them.
It often happens that an engine is observed to
draw a certain load on a certain inclination, and
to compare this work with that of another engine
which would perform another task on a difierent
inclination, it becomes necessary to refer each of
these loads to the level. We shall therefore begin
with this problem; that is to say, we shall seek
the means of passing from a given load, drawn
on a known inclination, to a train which would
offer an equal resistance on a level; and reci-
procally, from a known train, drawn on a level.
OF INCLINED PLANES. 471
to the load which, on a given inclination, would
offer an equal resistance.
Istly. Let us take the first case, and suppose the
practical inclination of the plane to be expressed
by-, that is to say, suppose its vertical elevation
to be to its length measured along the plane, in
the ratio of — Let M be the weight, in tons gross,
e
tender included, of the train placed on this inclined
plane ; and let fc be the friction of the waggons per
ton, expressed in pounds, as has been explained
Chapter V. Rnally, let m be the weight, expressed
in tons, of the engine which performs the traction.
With these notations, it is clear that fcM will
be the friction of the carriages of the train. More-
over, since 1 ton contains 2240 lbs., the gravity of
the train, plus the engine, will, as has been shown.
Chapter VI., be expressed by
2240 ^+"*.
e
Consequently, according as the engine has to ascend
or to descend the plane, the total resistance it meets
with from the train will be
fcM ±2240^ + ^.
e
Th^*efore the train which, on a level, would offer an
equivalent resistance, will have for its expression,
when the motion is ascending,
472 CHAPTER XVII.
k e
and when it is d
tr^y^i^t'.ttit
k e
If, for instanoe, thane be a load of 50 tons, toader
included, drawn up a plane inclined 9^, by an
engine of the weight of 8 tons, it will be found that
the equivalent load on a levd will be 86 tons ; and
if the traction takes place in descending, the equi-
valent load on a level will be no more than 14 tons.
The case of descending trains offers no more dif-
ficulty than that of ascending ones ; but it is to be
remarked that when
j^ 2240 M + m
"" k e
that \s to say, when the train , descends a plane
whose inclination is expressed by
1 k M
e 2240 M + m
the load which represents the resistance of the train
will become null. Thus, on the plane whose in-
clination we have just found, the friction proper
to the waggons will be exactly counterbalanced
by the gravity of the train augmented by that of
the engine. On any plane of greater inclination,
the resistance offered by the train, or the load M'',
will be found negative; that is to say, that so far
OF INCLINED PLANES. 473
from opposing the progress of the engine, the wag-
gons will tend on the contrary to urge it along the
plane, with a force represented by the negative
value thus obtained.
When therefore the inclination of the plane, the
weight of the waggons and that of the engine are
known, the load M'\ which would offer an equi-
valent resistance on a level, may immediately be
found.
2ndly. Suppose now that the result of an experi-
ment have made known the load M^^ which a given
engine can draw upon a level, and that it be desired
to deduce therefrom the load M which the same
engine could draw on a plane of a given inclina-
tion; then the preceding equation, resolved with
reference to M, will give, when the motion is as-
cending,
j^ eft M"- 2240 m,
~ e& + 2240 '
and when it is descending,
j^_efcM^^ + 2240m
~ eft -2240
It will be easy then to find the load M required.
If, for instance, we had found 86 tons for the load
of an engine on a level, it would be deduced from
thence that, on a plane ascending -^^^ and for an
engine of the weight of 8 tons, that load would
amount to 50 tons.
It will again be remarked here, that if the inclina-
tion of the plane in question be
474 CHAPTER XVII.
1 _ k M"
e ~ 2240 ' m '
and if the motioa take place in ascending, the load
which, on that plane, will correspond to the load
M" on a level, will be null. This circumstance
readily explains itself, on observing that we have
then
2240 m 1.,,,
-r'-e = ^ '
which indicates that, by reason of the inclination of
the plane, the gravity of the engine alone is equiva-
lent to the load M'^ on a level, and consequently all
that the engine can do will be to move itself up the
plane. If the inclination be greater than that which
we have just mentioned, a negative value will be
found for the load of the engine, which would arise
from the weight of the engine alone being already
too great to represent the load M""' on a level.
Finally, in the case in which the motion is de-
scending, and in which
1_ k
€ ~ 2240'
it will be found that the load of which the engine is
capable is infinite; and in effect the inclination of
the plane will be such, that the gravity of the wag-
gons will compensate their friction, so that they will
offer no resistance to the motion, and consequently
the engine may draw an unlimited number of them.
3rdly. Besides the two problems which have just
OF INCLINED PLANES. 475
occupied our attention, it may yet be required to
determine what is the inclination on which a given
load would be equivalent to another given load on a
level. This research offers no difficulty; for the
same relation obtained above, being resolved with
reference to - gives, when the motion is ascending,
1_ k M^^-M,
e ~ 2240 ' M + m '
and when the motion is descending,
1_ k M-M^^
e 2240 * M + m
In these two expressions, M still expresses the load
on the inclined plane, and M'^ the load on the level.
Thus, for instance, if we seek on what inclination
a load of 50 tons, drawn up an inclined plane by an
engine of 8 tons weight, is equivalent to a load of
86 tons on a level, we shall find the inclination of
the plane to be ^^.
It must however be observed, respecting the three
problems which have just been considered, that the
loads on a level, corresponding to loads on given
inclinations, are equivalent to them only as ^ as
they represent the traction and the gravity of those
loads ; thus far then they may replace each other,
but for this substitution to be exact, it must in no
way affect the resistance of the air, which is, always
to be valued by the number of waggons of the real
load, and not by the number of waggons which
476 CHAPTER XVII.
would compose the fictitious load, if it were really
to be drawn on a railway, practically and according
to the ordinary manner of loading.
For example, when a load on a level represents a
load drawn up an inclined plane, it is clear that its
weight must be greater ; and when it represents a
load drawn down the plane, it will on the contrary
have a less weight. In the former case, supposing
the load on a level effectually prepared for convey-
ance, it would require a greater number of carriages
than the real load, and in the latter case, it would re-
quire a less number. If then instead of computing
the resistance of the air according to the number
of carriages in the original load, it were valued ac-
cording to the carriages which the transformed load
supposes, the two loads thus considered would no
longer offer an equal resistance. When therefore
we say that two loads are equivalent to each other,
it is not to be understood that they can, always and
absolutely, replace each other, but merely that it is
possible at the same velocity and with the proviso
mentioned above.
Sect: II. Of the velocity of locomotive engines on
inclined planes.
When a locomotive engine draws a train up an
inclined plane, its velocity is necessarily diminished,
and on the contrary its velocity is augmented when
the engine draws its load down the plane. To be
OF INCLINED PLANES. 477
enabled then to form a complete judgment of the
influence of inclined planes on railways, it is neces-
sary to examine within what limits these effects of
diminution and increase of velocity are produced.
For this reason we are now about to consider the
motion of the engines, in ascending and in descend-
ing inclined planes.
When a locomotive engine ascends an inclined
plane, its load immediately becomes greater, because
the gravity of the train on the plane is added to
the friction of the waggons. One would then be in-
duced to think that the velocity must diminish in
a degree nearly proportionate; but that is not the
case, because, as the velocity of the engine di-
minishes, the resistance of the air diminishes very
rapidly, since it varies in the ratio of the square
of the velocity ; and consequently there remains in
the engine, so much the more force to apply to the
traction of the load. For the same reason, the
velocity, in descending inclined planes, does not
increase indefinitely, as might be thought at a first
glance.
This will easily be recognised on recurring to the
practical formula which we have presented in Article
III. of Chapter XII., for determining the velocity of
the engine, with a given load and on a known in-
clination, namely :
784 S
V=z _ _- .
(1-hd) [(6±y)M±5rm-hiit;2j -hF-h ?gi (2736-hyt;)
480 CHAPTER XVII.
Sect. III. Of the velocity of descent of trains^ an
inclined planes where no use is made of the force
of the engine.
The researches which have just engaged us are
relative to the ascent and descent of planes, on
which the force of the engine is used to produce
the motion of the train. This case invariably
occurs in all questions of ascent, but it obviously
does not always in questions of descent. In effect,
the latter may be divided into three classes :
1st. Inclinations on which the gravity is less than
the friction, and whereon the train could not
advance without the help of the engine ;
2nd. Inclinations on which the gravity exceeds
the friction, and whereon the trains would
descend of themselves, but with a velocity
less than what the work requires;
3rd. Inclinations on which the gravity so much
exceeds the friction, that the trains would
acquire too great a velocity during their de-
scent, if they were not restrained in their
motion by the use of the brake.
The first case is evidently comprised among those
which have been treated of in the preceding sec-
tion ; and it is the same with the two others, when-
ever it is thought prefer to use the force of the
engine, notwithstanding the inclination of the plane.
OF INCLINED PLANES. 481
In the second case, there may occur a problem
which we have not yet noticed : it is that of finding
what vaporization the engine ought to have, or to
apply, in order to communicate to the descending
train a determined velocity. This problem would
be solved by taking equation (7), Chapter XIII.
Sect. II., which gives the effective vaporization
of the engine for desired effects, and substituting
in it for the friction, gravity, &c., the data proper
to the inclined plane in question. It can therefore
offer no difficulty, and we shall dwell no longer
on it.
In the third case, it may be required to find what
velocity the trains would attain of themselves during
their spontaneous descent on the plane, and what
effort the brake ought to apply, to reduce their
velocity within certain fixed limits. This is the
object of our inquiry at present.
When the inclination of a plane is such that,
aided by the steam, the waggons would be liable to
acquire a greater velocity than would be thought
consistent with the safety of the passengers or the
preservation of the engine and carriages, the engme-
men suspend the action of the engine entirely. Then
the motion is nothipg more than the result of the
natural gravity of the train on the declivity, and it
is easy to obtain its valuation.
Suppose, in effect, the train to reach the summit
of the plane with the velocity, already considerable,
which results from the prior action of the engine ;
2i
480 CHAFTBR XVII.
Sect. HI. Of ike velocity of descent of Irakis, on
imclimed pUmet where no use is made of the force
of the engine.
The researches which have just engaged us are
rdative to the ascent and descent of planes, on
which the force of the engine is used to produce
the motioQ of the train. This case invariably
occms in all questions of ascent, but it obviously
does not alwajrs in questions of descent. In effect^
the latter may be divided into three classes :
1st. Indinations on which the gravity is less than
the friction, and whereon the train could not
advance without the help of the engine ;
2nd. Indinations on which the gravity exceeds
the fiiction, and hereon the trains would
descend of themselves, but with a velocity
less than what the work requires;
3rd. Indinations on which the gravity so much
exceeds the friction, that the trains would
acquire too great a velodty during their de-
scent, if they were not restrained in their
motion by the use of the brake.
The first case is evidently comprised among those
whidi have been treated of in the preceding sec-
tion ; and it is the same with the two others, when-
ever it is thought proper to use the force of the
engine, notwithstanding the inclination of the plane.
^
OF INCLINED PLANES.
481
In the second case, there may occur a problem
which we have not yet noticed : it is that of finding
what vaporization the engine ought to have, or to
apply, in order to communicate to the descending
train a determined velocity. This problem would
be solved by taking equation (7), Chapter XIII.
Sect. II., which gives the effective vaporization
of the engine for desired effects, and substituting
in it for the friction, gravity, &c., the data proper
to the inclined plane in question. It can therefore
offer no difficulty, and we shall dwell no longer
on it.
In the third case, it may be required to find what
velocity the trains would attain of themselves during
their spontaneous descent on the plane, and what
effort the brake ought to apply, to reduce their
velocity within certain fixed limits. This is the
object of our inquiry at present.
When the inclination of a plane is such that,
aided by the steam, the waggons would be Uable to
acquire a greater velocity than would be thought
consistent with the safety of the passengers or the
preservation of the engine and carriages, the engine-
men suspend the action of the engine entirely. Tboi
the motion is nothipg more than the result of^
natural gravity of the train on the decliviiy,
is easy to obtain its valuation.
Suppose, in effect, the train to readi (Ar
of the plane with the velocity, alreadr
suits from the prior actkm
.tu;.
/
i
A
k^
482 CHAPTER XVII.
it will first begin its motion on the plane with that
same velocity, and will tend to augment it more
and more, by reason of the constant action of the
gravity. But it is clear that, in this case, the
motive force will be nothing more than the excess
of the gravity, above the friction of the waggons
augmented by the friction of the engine; and the
resistance will be precisely the resistance of the air.
So long as the motive force predominates over the
resistance, the motion will continue to accelerate;
but as the motive force is constant, and as the
resistance of the air on the contrary increases
rapidly, there will be a point at which those two
forces will become equal ; and from that moment the
motion will be uniform. Considering, in Chapter V.,
the motion of bodies committed to gravity on in-
clined planes, we have shown that this uniformity
of motion will establish itself at the end of a limited
time.
If then the train be supposed to Jiave attained
that uniform motion, the resistance of the air will
be equal to the motive force. Now the motive force
is known, since it is no other than the excess
of the gravity above the frictions. Therefore the
excess of the gravity above tbe frictions will give
also the intensity of the resistance of the air during
uniform motion ; and consequently we may thence
deduce the velocity of that motion, or the velocity
which the train will necessarily acquire afler a
limited time of its descent. Hence, neglecting the
OF INCLINED PLANES.
483
difference which existed, at the commencement of
the motion on the plane, between the velocity of
the train resulting from the previous action of the
engine, and its definitive velocity residting from
gravity, we may take the uniform velocity which we
have just determined, as that of the whole passage
of that descent.
If, for example, we consider a train of 9 coaches
and tender, weighing 50 tons, preceded by an engine
weighing 8 tons, and suppose it placed on a plane
inclined xhf, the gravity of the train and engine
Yrill be 866 fts., the friction of the waggons will be
300 lbs., and that of the engine 100 fcs. nearly.
Thus the motive force, and consequently also the
resistance of the air during the motion, will be
466 lbs. Now the train offers to the resistance of
the air an effective surface of 170 square feet.
Hence the resistance of the air per square foot of
surface, will be 2*74 lbs.; which gives for the ve-
locity of the motion 31*94 miles per hour. If a
similar calculation be made, for different cases, the
following Table will be formed :
Velocity of descent of trains left to themselves on inclined
planes.
Deaignatioii of the tram.
Maximam velocity of the
train, in miles per hour, the
inclination of the plane being:
vvv
rsff
ToJf
Train of 50 tons, tender included
Train of 100 tons, tender included
23-40
26-21
31-94
3507
44-36
48-12
484 CHAPTER XVII.
Such are then the velocities the trains would attain
when abandoned to their own weight; but upon
railways a maximum velocity is fixed for the descent
of inclined planes, and that velocity is determined
with a view to the preservation of the railway and
carriages. If then we suppose that the greatest
velocity of descent on inclined planes has been
fixed at 26 miles per hour, as on the Liverpool
and Manchester Railway, it is plain that in the
different cases which we have just treated, the
engine-men will be obliged to use the brake, to
reduce the velocity to 26 miles per hour. Now as
the resistance of the air against a train of 10
coaches and the engine, at the velocity of 26 miles
per hour, is 309 fts., the effective motive force must
obviously, in all the cases, be reduced to that rate.
In practice, this effect will be produced by guess
and trial, by tightening the brake more or less ; but
it is easy to determine the friction which, in each
case, the brake ought to exert in order to obtain the
velocity desired. If, for instance, we consider the
train of 50 tons descending a plane inclined yfg^,
the effort of the brake must obviously be 466—309
= 157 lbs., and the calculation will be the same for
any other case.
These examples show that, whether the force of
the engine be employed wholly or partially, or the
trains be left to themselves, or their speed be
moderated by the application of the brake, it will be
easy, in all cases, to determine their velocity on the
inclined planes.
OF INCLINED PLANES. 485
The same Examples show that exaggerated fears
have been entertained, in France, of the dangers
which might result from the occurrence of declivities
on railways, and that it was carrying the precaution
too far to prohibit, in an almost absolute manner,
inclinations greater than the angle of friction, on
account of the danger to which they seemed to
expose the descending trains. This apprehension
was founded on the idea that, by the very fact of
the trains rolling spontaneously down the planes,
they might accelerate their velocity almost inde-
finitely. But the osculations which we have just
presented prove that, even though the brakes should
happen to give way, the velocity of descent of a
train of 100 tons, which is one of the heaviest in
use, would not exceed 48 miles per hour on an
inclination of you. Now this velocity is itself com-
prised within the limits that powerful engines attain
with light loads, and the Government has not as yet
deemed it necessary to interfere in this respect.
Besides, we have said that on rapid descents the
brake is applied ; and for above twelve years that the
Liverpool and Manchester Railway has existed, the
velocity of the heaviest trains has invariably been
reduced to 22 and 26 miles per hour, on planes
inclined ^ and ^, without any accident resulting
from that cause. We hope then the conviction will
prevail, that the only inconveniences attendant on
declivities consist in the surplus of work they
impose on the engines ; and in that respect, it is
486 CHAPTER XVII.
proper to leave to the companies who undertake
railways, the care of judging whether it is more
advantageous for them to make a tunnel or go
round a hill, rather than crossing it by means of an
inclined plane. But by refusing them the faculty of
employing the latter means, it has often happened
that expenses have been imposed on them, so heavy
as to amount almost to a complete prohibition of
the establishment of the railway.
Sect. IV. Of the duration of the trip, and of the
average velocity of the engines^ on a system of
sixcessive inclinations.
•
In the case of a train drawn on a railway which is
either level, or of a uniform inclination, there can
be no difficulty in finding the duration of the trip
from one point of the railway to another. In effect,
as the time employed by a body in traversing a
given space with a uniform motion, is equal to the
space traversed, divided by the velocity of the
motion, it will suffice, first, to determine the ve-
locity of the engine with the desired load, and then
to divide the whole length of the way by the ve-
locity of the engine, and the result will be the time
sought or the duration of the trip.
■
For example, if an engine is to traverse a space
of 30 miles, with a velocity of 10 miles per hour,
the duration of the trip of 30 miles will be
— = 3 hours.
OF INCLINED PLANES. 487
But if the line to be traversed consist of a series
of ascents and descents of various inclinations, the
question will become more complex, without how-
ever presenting more difficulty.
In this case, the velocity of the engine, Ynth the
given load, on each of the inclinations to be tra-
versed, must be sought, either by the formula
(1 bis). Chapter XII., or by the means indicated in
the preceding section ; then the separate lengths of
the inclinations must be divided, each by the re-
spective velocity of the engine, which will give the
time employed in traversing each inclination ; and
the sum of all the results thus obtained will be the
total duration of the trip. Finally, dividing the
whole distance by the total duration of the trip, the
quotient will be the average velocity of the trip.
If, for example, it were found that the engine
would perform 10 miles with the velocity of 10
miles per hour, 10 miles with the velocity of 20
miles per hour, and 10 miles at the velocity of 30
miles per hour, the total time of performing the
30 tniles would be
;0+ 10+ 10= 1-83 hour;
10 ^ 20 ^ 30
and consequently the average velocity on the whole
distance of 30 miles would be
30
= 16*4 miles per hour.
1-83
«
In general, if the successive lengths of the inclined
488 CHAPTER XVII.
planes to be traversed, be expressed by Lj, L,, &c.,
and the respective velocities of the engine on those
inclinations by V,, V„ &c., the time of performing
the whole distance will be
and the average velocity of the trip will be
L| + La + &c.
%+^-
This question then can offer no difficulty.
Among the applications relative to- this question,
we may have to consider a series of ascents and de-
scents between two points on a level, with a view
to determine what disadvantage there vfUl be, with
r^ard to the duration of the trip, and for an engine
and train of known weight, in following the undu-
lating line, instead of the straight and level line
which would join the two extreme points. This
problem occurs whenever, in projecting a railway, it
becomes necessary to choose between cutting through
a hill and crossing it by means of inclined planes.
In this case, the calculation will be similar to the
preceding. The velocity corresponding to the pas-
sage of the train over each inclination must be found
first, and after having deduced from it the time
employed in traversing all the inclinations, that time
must be compared with the time the engine would
require, according to equation (1 bis), to perform
OF INCLINED PLANES.
489
the straight and level Une which would join the
extreme points.
If, for example, it be desired to know the time of
traversing a total distance of 20 miles, and the
average velocity of the same engine, which has been
noticed in Sect. ii. of this chapter, with its load of
56 tons gross, tender included, in following either a
line entirely level, or a line of the same length, but
consisting of two equal and contrary incUnations,
referring to the velocities already obtained in Sect.
II., we shall form the following Table : —
Time of traversing 20 milesy and average velocity of a loco-
motive of 65 cubic feet of vaporization, with a load of
56 tons gross, on a system of equal ascents and descents.
•
Object of calculation.
Designation of the line to be traversed.
10 miles
on a level
and
10 miles
on a level.
10 miles
ascending
and
10 miles
descending
10 miles
ascending
and
10 miles
descending
10 miles
ascending
and
10 miles
descending
Time of traversrag 20
miles, in minutes .
Average velocity of
the trip, in miles
per hour
j 47-65
Us- 10
48-36
24-81
48-69
24-64
55-66
21-56
We see by these results, that on a system of
equal ascents and descents, compared with a level
line of the same length, the engine will always be at
a disadvantage with respect to the average velocity,
490 CHAPTEE XVII.
or the duration of the whole trip, 4since it here ap-
pears that the velocity, which was 25' 10 miles per
hour on a level, reduced itself successively to 24*81,
24*64, and 21*56, and the time of performing the
whole distance increases in a corresponding manner,
according to the system of planes over which the
engine has to pass.
It will be remarked at the same time, that it
would be quite inaccurate to take, as the average
velocity of the passage of the two inclinations, the
mean between the two velocities which we have
obtained in Sect, ii., for the ascent and descent
of those inclinations, because those two velocities
are not maintained by the engine during equal
times.
Sbct. V. Of the average load of the engineSy during
their passage over a system of successive planes.
When an engine ascends and descends several
successive inclinations, its load varies considerably,
since the gravity of the train now increases, qow
diminishes the original resistance of the train on a
level. It is necessary then to be able to calculate
the average load which results from these variations
during the whole time of the trip.
For this purpose it will suffice first to calculate,
by the means above indicated, the load on a level
which corresponds to the traction of the train over
each plane, and the time of traversing each respec-
OF INCLINED PLANES. 491
tive plane, that is to say» the time during which the
engine has to draw that load. Then, multiplying
each load by the time during which it is applied to
the engine, taking the sum of all these products,
and dividing that sum by the total time employed
in traversing all the planes, the result will be the
average load of the engine during the trip.
Suppose, in effect, the question concern a system
of two inclined, planes : one on which the load is
equivalent to 1 50 tons, and which requires 3 hours
of time; the other on which the load is equiva-
lent to 50 tons, and which requires 1 hour of
time. It is clear that during the first hour the load
of the engine is 1 50 tons ; during the second and
third, the load is still 150 tons; and during the
fourth hour, the load is 50 tons. Hence, during
each successive hour of the duration of the trip, the
loads will be
150 tons
150
150
50
500 tons ;
and as the total trip has had a duration of 4
hours, we see that the average load of the engine
during the whole trip, or per hour of work, will
be
^=125 tons.
492 CHAPTER XVII.
To obtain, therefore, the average load of the engine,
each effective load must be multiplied by the time it
is applied to the engine, the sum of all these pro-
ducts must be taken, and 'finally that sum divided
by the total time of the trip.
Thus, in general, expressing by Mi, M,, &c., the
successive loads of the engine on different planes,
by Li, La, &c., the respective lengths of the planes,
and by V„ V,, &c., the corresponding velocities,
h h &c
will be the times employed in traversing each of the
successive planes ; and
will be the average load of the engine during the
whole trip.
If the line in question consist of ascents and
descents traced between two points on a level, or of
ascents and descents counterbalancing each other,
the average load of the engine during its passage
over those inclinations, will always be greater than
it would be on the level line which would join the
two extreme points. In effect, if we first calculate
the effective loads, or the loads reduced to a level,
which correspond to the passage of an engine of the
OF INCLINED PLANES.
493
weight of 8 tons, drawing a train of 56 tons gross,
tender included, over divers given inclinations, we
shall obtain the following results : —
Effective loads of an engine of 8 tons weighty drawing a
train of 56 tons on divers given inclinations.
Direction of the
motion.
Effective load of the engine, in tons, the
inclination of the plane being :
0
-shv
tIt
^
Ascending
Descending
56
56
95-83
16-17
10917
2-83
215-33
-103-33
Then, recurring to the duration of the passage of
the same engine with its load over the different
planes, as obtained in the preceding section, and
proceeding, as we have just indicated, to find the
average load of the engine in ascending and de-
scending different planes successively, we shall ob-
tsdn the following Table : —
Average load of an engine of 8 tons weighty traversing ^ with
a train of 56 tons gross, a system of given ascents and
descents.
Object of calcu-
lation.
Average load, 1
in tons gross J
Designation of the line to be traversed.
10 miles on
a level and
10 miles on
a level.
56
10 miles as-
cending and
10 miles
descending
6104
10 miles as-
cending and cending
10 miles
descending
65-21
10 miles as
and
10 miles
descending
TtT'
127-37
494 CHAPTER XVII.
It appears, from these results, (hat there is always
a disadvantage in laying down a railway according
to a line of ascents and descents, instead of tracing
it according to the horizontal line which would join
the extreme points ; also that this disadvantage will
augment as the planes to be traversed are more
inclined, and that it will always subsist even for
planes less inclined than the angle of friction.
It will be remarked, that had we merely taken the
mean between the ascending and the descending
loads, on the different planes^ we should have had
56 tons, in every case, for the average load of the
engine. But that calculation would have been
faulty, since, if we take as an example the two
planes inclined 4^, the engine has to draw the load
of 109' 17 tons during 28*56 minutes, and the load
of 2*83 tons during only 20* 13 minutes ; and simply
taking the mean of the two loads, is by the fact
supposing that the two planes are traversed in equal
times.
Through not having made this distinction, some
engineers have thought that, as long as the inclina-
tions did not exceed that on which the waggons
run of themselves, the traction of the engines re-
mained the same as if the line were perfectly level.
As their practice was to compute the average load
by taking the mean between the ascending and the
descending loads, they concluded that the surplus of
traction in the one case was compensated by its
diminution in the other ; and thence the name of
OF INCLINED PLANES. 495
normal inclinations was given to inclinations less
than the angle of friction. But it is plain that no
inclination on a railway can be called normal, since
all slants, of whatever inclination they may be, are
disadvantageous in all cases. We have, in effect,
seen in the preceding section, that on a system of
ascents and descents of any kind, the average velo-
city of the engines with the same load is diminished,
or the time of traversing the same distance aug-
mented ; we here see that, on the same system of
planes, the average load of the engine per hour of
work is increased. On the other hand, it is obvious
that the useful effect definitively produced remains
always the same, since it consists solely in the con-
veyance of the load from one extremity of the line
to the other. There can be no doubt, then, that the
occurrence of ascents and descents on a railway is
disadvantageous in all respects.
Sect. VI. Of the quantity of work on a level, which
corresponds to the conveyance of a given load,
over a system of knoum inclinations.
There is yet another research which necessarily
presents itself with respect to railways consisting of
a series of different inclinations ; namely, that of the
quantity of work on a level, and at a Uke velocity,
which corresponds to the total work executed by the
engine during its trip. We mean to say that, when
an engine traverses a system of various inclinations,
496 CHAPTER XVII.
it performs, in traversiog each of those inclinations,
a certain quantity of work, which is measured by
the traction required of the engine and the length of
the inclination, or the distance on which that trac-
tion is exerted. When the engine then has finished
its trip, it has executed successively difierent quan-
tities of work ; and the object proposed is to find
the quantity of total work thus done by the engine,
and to deduce therefrom the work on a level, which
would be equivalent to it.
This problem occurs whenever, after having ob-
served the expenditure of fiiel of an engine, in
traversmg a system of planes with a given load, it is
required to deduce the expenditure of that fuel
which corresponds to the traction of 1 ton 1 mile
on a level. It is also the problem which occurs
when, after having observed the expenses of main-
taining and working the engines on a railway com-
posed of ascents and descents, it is required to
deduce what those expenses would be on a level
line.
To obtain the solution of this question, we must
first seek the quantities of work successively done
in the conveyance of the train on each inclination,
and their sum will give the work executed in the
whole trip. Comparing afterwards this work with
that which would be done in drawing a ton 1 mile
on a level, we deduce its expression in tons drawn
1 mile on a level.
Now, the force necessary to overcome the friction
OF INCLINED PLANBS. 497
of the waggons placed on the plane, is known.
Moreover, dividing the total weight of the train,
augmented hy that of the engine, and by that of the
tender, if the latter have not been originally com-
prised in the weight of the load, by the number
which represents the inclination of the plane, we
have likewise the gravity. We can therefore calcu-
late the traction required of the engine during its
passage over each plane, and multiplying that trac-
tion by the distance on which it is exerted, we have
the quantity of work performed during the passage
of the inclination. Making successively a similar
calculation for each plane, we may conclude the
total work demanded of the engine during the whole
trip ; and, finally, knowing that the draught of a
ton 1 mile on a level requires a traction of 6 fts.
1 mile of distance, or a quantity of work of 6 fts.
raised 1 mile, we may definitively deduce the work,
on a level, which corresponds to the total work of
the engine.
To simplify this calculation, instead of seeking
immediately the definitive work required of the
engine on each inclination, by virtue of the friction
and the gravity, we may, which amounts to the
same, calculate first the work performed in over-
coming the gravity of 1 ton on each successive in-
clination. Then, having once found this work, ex-
pressed in pounds raised 1 mile, knowing also that
a weight of 6 fts. is equivalent to the traction of
1 ton on a level, we may immediately express it in
2k
496 CHAPTER XVII.
it perforins, in traversing each of those inclinations,
a certain quantity of work, which is measured by
the traction required of the engine and the length of
the inclination, or the distance on which that trac-
tion is exerted. When the engine then has finished
its trip, it has executed successively different quan-
tities of work ; and the object proposed is to find
the quantity of total work thus done by the engine,
and to deduce therefrom the work on a level, which
would be equivalent to it.
This problem occurs whenever, after having ob-
served the expenditure of fiiel of an engine, in
traversing a system of planes with a given load, it is
required to deduce the expenditure of that fuel
which corresponds to the traction of 1 ton 1 mile
on a level. It is also the problem which occurs
when, after having observed the expenses of main-
taining and working the engines on a railway com-
posed of ascents and descents, it is required to
deduce what those expenses would be on a level
line.
To obtain the solution of this question, we must
first seek the quantities of work successively done
in the conveyance of the train on each inclination,
and their sum will give the work executed in the
whole trip. Comparing afterwards this work with
that which would be done in drawing a ton 1 mile
on a level, we deduce its expression in tons drawn
1 mile on a level.
Now, the force necessary to overcome the friction
OF INCLINED PLANBS. 497
of the waggons placed on the plane, is known.
Moreover, dividing the total weight of the train,
augmented by that of the engine, and by that of the
tender, if the latter have not been originally com-
prised in the weight of the load, by the number
which represents the inclination of the plane, we
have likewise the gravity. We can therefore calcu-
late the traction required of the engine during its
passage over each plane, and multiplying that trac-
tion by the distance on which it is exerted, we have
the quantity of work performed during the passage
of the inclination. Making successively a similar
calculation for each plane, we may conclude the
total work demanded of the engine during the whole
trip ; and, finally, knowing that the draught of a
ton 1 mile on a level requires a traction of 6 fts.
1 mile of distance, or a quantity of work of 6 fts.
raised 1 mile, we may definitively deduce the work,
on a level, which corresponds to the total work of
the engine.
To simplify this calculation, instead of seeking
immediately the definitive work required of the
engine on each inclination, by virtue of the friction
and the gravity, we may, which amounts to the
same, calculate first the work performed in over-
coming the gravity of 1 ton on each successive in-
clination. Then, having once found this work, ex-
pressed in pounds raised 1 mile, knowing also that
a weight of 6 lbs. is equivalent to the traction of
1 ton on a level, we may immediately express it in
2k
498 CHAPTER XVII.
tons drawn 1 mile on a level. After having ob-
tained this expression for each of the successive
planes, nothing remains but to take the sum of
these expressions, in order to have the total work
resulting from the draught of 1 ton over all the
planes of the whole line. Consequently, multi-
plying this result by the number of tons which
compose the total mass in motion, and adding to it
the work done in overcoming the resistance of the
air and the friction of the waggons, on the total
length of the trip, we shall have definitively the
work performed in the traction of the train over all
the planes of the whole line. It is necessary only,
before going any farther, to add here two observa-
tions.
Tlie furst is, that it is proper to distinguish the
ascents from the descents, and, to that end, care
must always be taken to give to the work done in
overcoming the gravity, the sign plus for those por-
tions of the Une which are to be ascended, because
on those portions the gravity, and consequently the
work which represents it, is to be added to the
traction of the waggons; and the sign minus for
those portions of the line which are traversed in
descending, because on descents the gravity, on the
contrary, comes in deduction of the work required
of the engine, and is consequently to be subtracted.
By this means, we have only to add, with their
sign, all the quantities of work thus found, in order
to deduce the definitive work done in overcoming
OF INCLINED PLANES. 499
the gravity of 1 ton on the whole line of inclina-
tions.
The second observation which we have to make is
relative to planes more inclined than the angle of
friction. It is known that on these planes the
gravity exceeds the friction, so that the train might,
in fact, continue its motion without the help of the
engine. However, as for a railway enterprise it is
not enough that the train move slowly onward, but
it must assume and maintain the velocity fixed by
the exigencies of the trade ; as, moreover, the train
cannot run of itself at any velocity on a descent,
unless the gravity be capable of overcoming not
only the friction of the waggons but that of the
engine, it follows, finally, that it is only on planes
sufficiently inclined for the gravity to be equal to
the ^um of the friction of the waggons, the friction
of the engine, and the resistance of the air against
the train at the desired velocity, that the effect of
the engine can be dispensed with.
According to the velocities in use on railways at
the present day, 25 miles per hour may be con-
sidered as the velocity generally adopted for a train
of 10 carriages or 50 tons gross, exclusive of the
tender, and about 20 miles per hour for that of a
train of 20 waggons or 100 tons gross, exclusive of
the tender. Admitting then these data, and taking,
besides, 100 fts. for the friction proper to an engine
of 8 tons, it appears that the inclinations on which
it would be possible to suspend the action of the
500 CHAPTER XVII.
steam will be -^^ in the first case, and t^t ^^ ^^
second. It may then be admitted, on an average,
that, on a well-kept railway adapted to ordinary
velocities, with well-constructed carriages, the trains
will of themselves acquire a sufficient velocity, when
the inclination is -3^ ; so that on such inclinations
the action of the steam may be entirely suspended.
This premised, it is visible that in seeking the quan-
tities of work done by the engine in traversing a
system of divers planes, we must set down zero for
all descending planes inclined -3^ or more ; that is
to say, we must, for those planes, omit in the calcu-
lation both the gravity of the mass and the friction
of the waggons, since these two quantities mutually
destroy each other.
To give an example of this calculation, and to
render the explanation of it perfectly clear, we will
seek the quantity of work done by the locomotive
engines of the Liverpool and Manchester Railway, in
the conveyance of their load over the totality of the
space which they have to traverse. As the calcula-
tion relative to the gravity is performed much more
commodiously by way of a Table, we will here pre-
sent it under that form. The first column of the
Table contains the successive lengths of the line, the
second indicates the respective inclinations of each
of those distances, the third gives the gravity of 1
ton on the inclination considered ; the fourth and
last contains the product of that gravity by the
distance traversed, that is, the work done in over-
OF INCLINED PLANES.
501
coming the gravity ; but, having been divided by 6,
this work is transformed into tons drawn 1 mile on
a level.
Tlie signs placed before the numbers mark, as we
have just said, the ascending or the descending
planes. Thus the inclination f^^ is a descent in
going from Liverpool to Manchester, and therefore
the work corresponding to the gravity has the sign
minus; but it is an ascent when the line is traversed
in the opposite direction, which causes it, in that
case, to have the sign plus. The gravity on the
inclinations ^"^ and ^^-^ might have been neg-
lected in this calculation, because in practice these
inclinations may be treated as level Unes.
Work done in overcoming the gravity on the Liverpool and
Manchester Railway.
Section of tbe railway, from
LiTerpooI towards
Manchester.
Distances.
miles.
•53
5-23
1-47
1-87
1-39
2-41
6-60
5-62
4*36
29-48
Inclinations.
d.
a.
0
1
0
1
TV
d.
d.
Gravity of 1
ton on the
inclination
traversed.
tbs.
0
2-04
23 33
0
2500
•81
2-64
1-72
•52
Work done in overcoming
the gravity of 1 ton
From Liver-
pool towards
Manchester.
tons 1 mile on
a leveL
0
-1-78
-f5-71
0
- -32
-2-90
+ 1-61
+ -38
+ 2-70
tons 1 mile on
a leveL
0
-f 1-78
From Man-
chester
towards
liverpooL
f»
0
+5-79
+ -32
+ 2-90
-1-61
- -38
+ 8-88
502 CHAPTER xvir.
This Table shows that the gravity of each ton of
a train drawn from one end to the other of the
Liverpool and Manchester Railway, requires from the
engine, according to the direction of the motion, a
quantity of work equivalent to 2*70 or 8'88 tons
drawn 1 mile on a level. Ebcpressing then by M,
the weight of any train, by m the weight of the
engine, and by C the weight of its -tender supposed
not included in the load Mj, the work done in over-
coming the gravity of the train on the line, will be
From Liverp. to Manch. . . 2*70 (M, -f- C -f m) tons 1 mile;
From Manch. to Liverp. . . 8'88 (M, -f- C -f m) tons 1 mile.
But on the other hand, laying aside the descents
more inclined than -j^, on which the engines are
not made to work, the distance performed by the
trains is 28*09 miles from Liverpool towards Man-
chester, and 28*01 miies in the contrary direction;
and the friction of the carriages is to be overcome
by the engine throughout the extent of this distance*
Therefore, the quantity of work done in overcoming
the friction of the carriages, for a load of M, -|- C
tons drawn from one end of the line to the other,
will be
From Liverp. to Manch. . . . 28*09 (M, + C) tons 1 mile ;
From Manch. to Liverp. . . . 2801 (M, -f C) tons 1 mile.
Hence, finally, adding the work done in overcoming
the gravity to that which is done in overcoming the
friction, the total work performed by the engine, in
OF INCLINED PLANES. 503
the conveyance of the load Mi along the whole line,
will be
From Liverp. to Manch. . . 30'79 (Mj +C) +2-70 m tons 1 mfle.
From Manch. to Liverp, . . 36-89 (Mi +C) +8*88 m tons 1 mile.
In these expressions, m represents the weight of the
engine effecting the motion. It is understood then
that if the train is drawn by two or more engines, m
is to be replaced by the weight of those different
engines united. Similarly, if a train is helped in
a part of the trip by an assistant engine, the above
quantity of work must receive an addition, corre-
sponding to the gravity of the assistant engine and
its tender, on the portion of the line which it has to
traverse, and to the friction proper to that tender on
the same distance. On the Liverpool and Man-
chester Railway, for ascending the two planes in-
clined ^ and ^ , assistant engines are used, weigh-
ing with their tender about 18 tons. The addition
to make on that account, for friction and gravity, is
therefore, very nearly, 112 tons one mile in each
direction ; but as the assistant engines are used only
for about half the number of the trains, allowance
will be made for this circumstance by adding only a
work of 56 tons one mile, for each train conveyed
along the line. Consequently, observing finally
that the average weight of the engines is 8 tons,
and that of the tenders 6 tons, which gives m = 8,
C = 6, we find that the work done by the engines,
exclusive of the resistance of the air, in the convey-
504 CHAPTER XVII.
ance of a train of M, tons along the whole line, is
represented by the two following expressions : —
From Liverp. to Manch. . . . 30*79 M^ -f 262 tons 1 mile ;
From Manch. to Liverp. . . . 86'89 M, + 348 tons 1 mile.
It is, however, to be remarked, that the result
thus obtained only represents the work executed in
the conveyance of the load, as taken independently
of the resistance of the air against the train, and of
divers other resistances which the engines have to
overcome, such as their own friction, their additional
friction, the pressure arising from the blast-pipe, &c.
This result is to be considered, then, only as a rough
estimate, whereon to ground approximate calcula-
tions, such as may in general be deemed sufficient in
practice, but not as an exact and mathematical ex-
pression of the work executed in the motion of the
train. The result of this research will nevertheless
be rendered much more exact, by adding to the
work done in overcoming the friction and gravity^
that done in overcoming the resistance of the air
against the train at the velocity fixed upon for the
motion.
Thus, taking 22*5 miles per hour, as the average
required velocity on a railway for general transit,
and 15 carriages, exclusive of the tender, as the
average load, we find that the resistance of the
air against the train in motion will be 327 lbs.,
which is equivalent to the traction, on a level
and at very little velocity, of a weight of 55 tons
OF INCLINED PLANES. 505
gross. This traction is to be performed by the
engine throughout all the length of the portions
of the railway on which the action of the engine
is not suspended. Consequentiy, in the case of
the Liverpool and Manchester Eailway, and at the
above velocity, the resulting addition, in either
direction, will be 1543 tons one mile; and thus
the work done in conveying the load Mj, from
one end of the line to the other, including the
resistance of the air at the average velocity of 22*5
miles per hour, will be
From liverp. to Manch 30*79 M^ + 1805 tons gross 1 mile
on a level, at very
little velocity.
From Manch. to Liverp 36'89 M^ + 1891 tons gross 1 mile
on a level, at very
little velocity.
The calculation which we have just performed
would equally apply to every other line, with this
difference, that if the velocity necessary for the
conveyance were less than 20 to 25 miles per
hour, as we took it above for railways of great
velocity, the action of the engine might be sus-
pended on descents of less inclination than so^;
and then, in the calculation of the work done by
the engine, all the motion performed in descending
inclinations thus fixed for the limit of the use of
the engine, must be suppressed.
As a second example of the preceding calcula-
tion, we will seek the quantity of work executed
506 CHAPTER XVII.
by the engines of the Stockton and Darlington
Railway, in the conveyance of a train of waggons
along that line. This research, besides, will be
needM to us in the Appendix to this work, for
deducing the expense of carriage on that railway.
We give, in the annexed Table, the section of the
portion of that line traversed by the locomotives,
and the quantity of work done in overcoming the
gravity. As the speed on that railway is but 8
miles per hour, and the trains are composed of
24 waggons, which, with their load, weigh 95 tons
gross; as the average weight of the engines is
10*5 tons, and that of their tenders 4*5 tons;
and as, finally, the friction of the engines, which
are but little taken care of on that line, may be
estimated at 30 lbs. per ton instead of 15 lbs., we
find that the inclination which is sufficient to make
the trains descend, with the velocity fixed for the
work, is -g^. Taking account then of this limit,
to deduct from the total trip the planes traversed
without the help of the engine, we form the follow-
ing Table :
OF INCLINED PLANES.
507
Work done in wercoming the ffraviiyy an the Stockton and
DarKngton Railway {portion traversed by the hcomo-
tives).
Section of the railway from
Bnuaelton to Stockton.
Work done in oyercoming the
gravity of 1 ton.
Distances to be
traversed.
Corresponding
inclination.
From Bnissdton
to Stockton.
From Stockton
to Brusselton.
miles.
•46
•06
•92
1-45
2-25
1-25
101
1-76
•20
1^75
1-61
1-64
•23
209
1-25
•03
•81
•05
•80
M6
d. TTT
d. rh
d. rhr
d. yfr
d. rh
d. Tir
d. Tir
d. rir
d. -rh
d-TsVa:
d. rhr
d. -air
d. 7+T
d-TiVs
d. Tir
0
d. TTTT
d. xfr
d iVrj
d. T*X
tons 1 mile.
- -552
- 069
0
0
-1-591
0
-1-071
0
- -189
- ^412
- -427
0
- -120
- -356
0
0
0
- 038
- -189
0
tons 1 mile.
-h 552
+ ^069
-f 2^385
-f 4-474
H- 1-591
+ 3-457
-f 1071
+ 4-867
-h -189
+ -412
-h -427
+ 3001
+ -120
+ ^356
H- 1-845
0
+ r338
H- ^038
-f -189
-f 4^164
20^78
-5014
+ 30-545
Consequently, calculating, as we did above, for
the Liverpool and Manchester Railway, we find that
on that portion of the railway from Stockton to
Darlington on which the locomotives run, the con-
veyance of any load Mj, expressed in tons gross,
exclusive of tender, requires of the engines, inde-
508 CHAPTER XVII.
pendently of the resistance of the air, a quantity of
work represented, in tons drawn 1 mile on 4 level,
by the foUowing expressions :
From Bmsselton to Stockton ... 5' 5 M, — 28 tons gross 1 mfle
on a level ;
From Stockton to Bnusdton . . 51*33 M^ +552 tons gnMs 1 mfle
on a level.
If it be desired, moreover, to introduce in the
calculation the resistance of the air against the
trains, the work done by the engines in drawing
a train of 24 waggons at the velocity of 8 miles per
hour, will be
From Bmsselton to Stockton ... 5* 5 M^ + 70 tons gross 1 mfle
on a level, at very
little velocity.
From Stockton to Bmsselton . . 51*33 M^ +745 tons gross 1 mile
on a level, at very
little velocity.
It is to be remarked, that when, in calculations of
this kind, there occurs an incline followed by an
equal contrary incline, and when their inclination
is not sufficient for the action of the steam to be
dispensed with during the descent, the computation
of the definitive work done by the engine in tra-
versing the two inclines wiU give the same number
as if the line had been level. It is thence to be
concluded, that taking, as we have done, the re-
sistance of the air at its average value on all the
portions of the trip, the work done in the convey-
ance of the train on the two inclines will be the
OF INCLINED PLANES. 509
same as on a level. But this result arises simply
from this, that in supposing the resistance of the
air constant, we make a supposition favourable to
the case of ascents and descents. In effect, if we
refer to Sect. ii. of the present chapter, and seek
the resistance of the air against a train of 56 tons
gross drawn by a locomotive of 65 cubic feet of
vaporization, traversing either a level line or a
system of given ascents and descents, we shall in-
variably find that the resistance of the air is less on
the level line, though the average velocity is greater ;
and this is occasioned by the resistance of the air
increasing as the square of the velocity. Thus, for
instance, on two slants inclined x5T5r> the velocities
of the train will be successively 14"90 and 40*00
miles per hour, which, for 10 carriages besides
engine and tender, will produce a resistance of the
air, first of ll4fts. and afterwards of 817, or at a
medium 465 fts. ; and on the level portion, at the
velocity of 25*10 miles per hour, the resistance of
the air will be only 319 fts.
We are then finally to conclude, from the divers
researches relative to ascents and descents, com-
pared with the same length of road traversed on a
level :
That on a system of ascents and descents, the work
performed by the gravity of the train in descending
an incline, may compensate the work required from
the engine by that same gravity in ascending the
contrary incline ; but that in taking account of all
510 CHAPTER XVII.
the drcumstances of the motion, the average velo-
city of the engine will be reduoed, its average load
augmented, and the duration of the trip increased ;
whence will result a loss of time, more wear and
tear of the engine, and an increased consumption of
fuel.
Sect. VTI. Of the means of ascending inclined planes
on railways.
From what has just been seen, inclined planes are
always a great obstacle on railways ; they diminish
the velocity of the conveyance, and augment the
average traction of the engine. Besides this, to be
enabled to ascend them, it is necessary to reduce the
load of the engines below what they could draw on
a level ; and we have seen that, with regard to fiiel,
the engines work to greater advantage inasmuch as
their load is greater. Finally, the use of the brake
in descending inclined planes causes rapid destruc-
tion of the rails. It is therefore very important, in
establishing a railway, to avoid inclined planes as
much as possible.
When, however, incUned planes are unavoidable,
there are four means of effecting the passage over
them : 1st, by employing a stationary steam engine,
which performs the traction of the train by means
of ropes ; 2nd, by employing an assistant locomotive
engine, which pushes the train from behind and
drives it to the summit of the plane ; 3rd, by raising
OF INCLINED PLANES. 511
the pressure of the steam in the holler of the engine
so, as to make it capable of a greater effort, with a
proportionate diminution of velocity ; and 4th, by
reducing the load of the engines so as to enable
them to ascend the planes without additional help.
Stationary engines always obstruct in some way
the prompt execution of the work, and they expose
the trains to accident, if the rope used for the trac-
tion should happen to break. Assistant engines,
which want a fire kept up, even in the intervals of
their work, are an increase of expense to the com-
panies, and consequently oblige them to raise their
prices. The augmented pressure in the boiler is
dangerous to the safety of the engines and the pas-
sengers. Finally, the diminution of the load is a loss
to the companies, since more trips are required to
perform the same work.
When, therefore, a railway contains indined
planes, we have only the choice of the inconve-
niences, and it is only by an attentive examination
of the circumstances of each particular case, that
the best mode of traversing them can be decided
upon. Some general ideas, however, on this sub-
ject, may be formed beforehand, by considering the
surplus of traction required by a given inclination.
1st. On a plane inclined y^o the gravity of 1 ton
is 22 fts., that is to say, about four times the friction
proper to the waggons. The resistance opposed to
the motion becomes then immediately five times as
much as it was on a level. Besides, the engine
512 CHAPTER XVII.
must overcome its own gravity, which, for an engine
of 12 tons, amounts to 269 fts. ; but as, on the other
hand, the diminution of the velocity of the train, in
ascending the incline, immediately produces a reduc-
tion in the resistance of the air and in that arising
from the blast^pipe, we will neglect at the same
time these opposite circumstances. Thus, the train,
as soon as it reaches the foot of the ascent, offers
about five times its resistance on a level ; and con-
sequently, if the engine be supposed to have pre-
viously drawn its full load on a level, there will
need five engines to get that load to the top of the
plane. Now, it is readily conceived that, to prevent
the expenses from becommg too great, the passage
of ascents ought in no case to require more than
one assistant engine. It is evident, besides, that this
can take place on an inclination of y^, only when
the load given to the engines is limited to about
half what they could really draw on a level ; for,
being once arrived at the foot of the plane, that load
becoming five times as great, will be 2^ times the
maximum load of which the engine is capable, and
consequently an assisting engine somewhat stronger
than the trip engine will suffice to drive the train
to the summit of the plane. Thus, we see firstly
that a plane inclined ^hs ^^^y he traversed by means
of one assistant engine, provided the load imposed
on the engines be not greater than about half their
maximum load.
2nd. Should the ascent be inclined more than
OF INCLINED PLANES. 513
x^i it might still indeed be traversed with a single
assistant engine; but then it is obvious that the
load of the engines on a level must be reduced
below what we have just supposed ; and there would
no doubt be few cases, at least on railways destined
to the simultaneous conveyance of goods and pas-
sengers, on which it would be found advantageous
to fix the load of the engines below the half of their
maximum load. We may therefore say generally
that an inclination of xoir ^iU be nearly the limit of
ascents on which assistant engines may be employed,
and that, for greater inclinations, recourse must be
had to stationary engines.
3rd. On a plane inclined ^^, the gravity of a
ton is 7*50 fts., and consequently the total resist-
ance of the train becomes about double what it
would be on a level. An engine may then without
assistance ascend an acclivity of that inclination,
provided its load on a level do not exceed the half
of what it might be. We may therefore consider a
plane of this inclination as being nearly the most
inclined that can be admitted on a railway without
being constrained to employ assistant engines.
Thus, we are led to the following general con-
clusions : —
1st. On planes whose inclination does not exceed
•3^, the traction may be performed without ad-
ditional help ;
2nd. On inclinations comprised between y^ and
2l
514 CHAPTBR XVII.
XoiTf it will generally be necessary to have recourse
to assistant engines ;
3rd. On planes more inclined than t^* it will
most commonly be found advantageous to employ
stationary engines.
Nevertheless we here repeat that the attentive
examination of the circumstances of each case, can
alone fix the choice in a decisive manner, and it is
only with a view to indicate how that examination
should be proceeded in, that we have entered into
the foregoing considerations.
Sect. VIII. Of the best line for a railway between
two given points.
Finally, before terminating this chapter, we have
still a question to treat of, namely : the choice to
be made between divers lines, with ascents and
descents, proposed for a railway to be established
between two determined points.
What has been said of the velocity, the duration
of the trip, and the effective load of the engines,
on a system of ascents and descents, includes all the
elements of calculation that the present question re-
quires ; for, supposing the different plans executed,
and the projected lines traversed by the same loco-
motive engine, with the same load, we may imme-
diately find the average velocity which would take
place on each, the time of traversing its total length,
and, lastly, the quantity of work done by the engine
OF INCLINED PLANES. 515
in the conveyance of a given load from one ex-
tremity of the line to the other. This question,
therefore, offers no remarkable difficulty; but to
fiidlitate its solution, we think it useful to explain
more precisely the proceeding to be followed.
In order to solve the question proposed, the fol-
lowing way may be used :
Ist. Since the nature and quantity of the goods
to be carried are known, the number of trips pei^
day will be fixed first of aU, and consequently
the average load which the engines will have to
draw. This done, in recurring to the considera-
tions presented in Chapter XIII., the width of way
to be adopted will be decided upon, as well as the
dimensions and weight of the locomotive engines
to which it may appear advisable to give the pre-
ference.
2nd. A Table of the velocity, the time of tra-
versing 1 mile, and the load on a level, of the
engine, when passing, with its train, over divers
planes more or less inclined, will be calculated.
Afterwards, having the section of the different
lines proposed, one of them will be adhered to;
then taking successively each of its inclinations,
and seeking in the Table the inclination which
approaches nearest to the one considered, there
will be found annexed to it the velocity, the time
of traversing 1 mile, and the corresponding load
of the engine. Consequently, multiplying the time
of traversing 1 mile by the length of the plane, we
516 CHAPTER XVII.
shall have the time employed in traversing that
plane; and multiplying the load on a level, by
the same distance, we shall have the quantity of
work done by the engine in traversing the plane
in question.
Performing therefore the same operation for all
the different planes which compose the line, taking
the sum of all the partial times employed to cross
these planes, and of all the quantities of work ex-
ecuted by the engine, we shall have the total dura-
tion of the trip over the line considered, and the
total work done in the conveyance of the load from
one end of that line to the other.
Thus, operating in the same manner for the dif-
ferent lines proposed, we shall have the total dura-
tion of the trip over each of them, and the quantity
of work, in tons drawn 1 mile on a level, done by
the engines in the conveyance of the determined
load between the two given points. Afterwards,
multiplying this last number by the amount of the
expense of draught per ton per mile on a level, as
will be indicated in the Appendix, we shall have
the expense necessary for the traction on the line ;
adding thereto the other accessory expenses, which
will likewise hereafter be given, we shall conclude
the total expense of working the line ; and lastly,
computing the interest of the capital necessary for
the execution of each line, and adding it, we shall
have the total amount of expense corresponding to
each line proposed.
OF INCLINED PLANES. 517
Thus, with regard both to the duration of the trip
between the two given points and the expenses of
the work, every means will be afforded of com-
paring together the different lines projected.
To show the manner of forming the practical
Table just mentioned, we will suppose to have been
adopted a way 5 feet wide, an average load of 50
tons gross, exclusive of tender, and a locomotive of
65 cubic feet of vaporization with the dimensions
indicated in Article III. Chapter XII., excepting the
pressure in the boiler, which we will suppose 70 fts.
per square inch. With these the following Tables
will be formed, and employed as has been indicated
above.
518
CHAPTER XVII.
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OF INCLINED PLANES.
519
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520 CHAPTER XVII.
In making the requisite comparisons between
different lines proposed, the above Tables may be
used, without calculating them again especially for
eack came. It must only be observed, that the Tables
are strictly exact for the case of a way 5 feet wide,
a load of 50 tons, and an engine similar to the engine
supposed. Consequently, in the question of a rail-
way on which other loads or other engines are in-
tended, the comparison by means of these Tables
must no longer be considered in any other light than
as an approximation, that may require to be con-
firmed by an ulterior calculation. In the case then
wherein such confirmation should seem necessary,
the calculation must be repeated with more pre-
cision, taking for each proposed line its true inclina-
tion, and applying even to each line the width of
way, the load, and the locomotive likely to give the
most advantageous results. For those calculations
we refer to what has been said in the different
sections of this chapter.
In the preceding Tables, we have supposed the
engine to have help, as soon as its velocity, on the
ascents, should lower to about 1 5 miles per hour ;
the action of the steam to be suspended, on the
descents, as soon as the velocity should tend to ex-
ceed about 30 miles ; and, lastly, the brake to be
used, to limit the speed to that rate, on all descents
whereon the trains would of themselves assume too
rapid a motion. These are, in fact, the limits gene-
rally adopted on railways at this time.
CHAPTER XVIII.
OF CURVES.
Sect. I. Of the effects of curves on railways.
Curves in railways present inconveniences which
are by so much the greater as their degree of curva-
ture is greater.
These inconveniences are of three kinds: 1st.
When a waggon moves in a curve, the wheel which
follows the outer rail necessarily goes over more
groimd than that which follows the inner rail.
Now, in waggons at present in use, the two wheels
of the same pair are not independent of each other,
but are fixed invariably on the axle which turns
with them. Therefore the distance described by
the one cannot be less than the distance described
by the other, except the latter be drawn without
turning over the difference between the two distances
to be described. This is in consequence an addi-
tional resistance offered to the motion.
2nd. The centrifugal force created in the passage
of the curve, by virtue of the velocity of the motion,
may urge the waggons outwards, so far as to pro-
duce a contact and consequently a friction of more
or less energy of the flange of the wheel against the
522 CHAPTER XVIII.
outer rail; and the resistance produced by this
cause is much more injurious than the former one,
because the friction takes place on the whole of the
distance performed by the wheel, and not merely on
the difference of the distances performed by the two
wheels.
3rd. Finally, the centrifugal force of the motion
may be such as not only to press the flange of the
outer wheel against the outer rail, but by pushing
the wheel violently in a direction tangential to the
curve, it may drive the flange of the wheel over the
rail, and thus throw the train out of the rails.
We are about to consider successively these dif-
ferent effects of curves.
Sect. II. Of curves the resistance of which is cor-
rected by the conical inclination of the wheels of the
waggons.
The wa^on wheels in use on railways are not of
a cylindrical form. On railways of about 5 feet
width of way, they are made of 3 feet in diameter
at their inner edge, near the flange, and 2 feet
11 inches at their outer edge. The wheel is ori-
ginally cylindrical, but the conical inclination is
produced by the addition of a tire or band of wrought
iron, which gives to the wheel its definitive diameter,
and whose thickness on one side is half an inch less
than on the other. Figure 29 represents the shape
of this tire on a scale of i of its real size. The
OF CURVBS. 523
width of the tire being 3^ inches, its conical inclina-
tion is ^ inch on 3^ inches, or ^.
The original object of this form of wheel is to
prevent a strong side wind, or the accidental de-
pression of one of the rails, from driving the wag-
gons on one side of the road, and thereby producing
a friction of the flange of all the wheels of that side
against the lateral surface of the rail, that is to say,
a considerable resistance against the motion. By
means of the above-mentioned disposition, this
lateral displacing of the train becomes more dif-
ficult ; and if nevertheless, from any cause, it do
take place, and the waggons have been momentarily
thrown on one side of the railway, the wheels on
that side immediately increasing in diameter, begin
to advance quicker than those on the opposite side,
and consequently bring back the train to its normal
position between the rails.
The conical inclination of the wheels suffices, of
itself, to remedy the inconveniences of the passage
over curves, when the degree of curvature of the
latter does not exceed certain limits. In effect, if
the two rails of the road be supposed exactly level
one with the other, it is plain that in the passage
along the curve, the centrifugal force of the motion
will drive the waggon towards the outer rail. But
gradually as the waggon is thus laterally displaced,
the wheel on the outer side turns, by reason of its
conical form, on a circle of still greater and greater
diameter, and the inner wheel, on the contrary,
turns on a diameter still less and less. In this state
524 CHAPTER XVIII.
of things, the two wheels of the same pair assume,
by the fact, different diameters. Moreover, it is the
outer wheel which acquires the greater diameter, or
which performs the greatest distance in the same
time ; consequently the waggon now tends, of itself,
to turn in the direction of the curve. It will readily
then be conceived how this disposition of the wheels
may remedy the inconveniences of certain curves,
but it will now be proper to particularize still
further the effects which are then produced.
The calculation of these effects evidently depends
on two things : the intensity of the centrifugal force
produced by the motion of the waggons in the curve,
and the intensity of the centripetal force produced
at the same time by the inequality of the wheels of
the waggons. We shall then, first of all, call to
mind the value of those two forces.
The centrifugal force, in the curve whose radius
of curvature is p, has for its expression, representing
the velocity of the motion by V, and the mass of the
moving body by m,
/=m — ;
P
but P being the weight of the same body, and g the
accelerating force of gravity, we have
P = 5riw, whence m = -.
Therefore the centrifugal force has also the value
P V^
J • 9
9 P
OF CURVES. 525
which is the expression of the centrifiigal force for a
body of a given weight P, set in motion with the
velocity V, in a curve whose radius of curvature
is p.
In this expression, g is the accelerating force of
gravity, or, as is well known, double the space
described in the unit of time by a falling body in a
vacuum. Taking the second as the unit of time, and
the English foot as the unit of space> we have
g = 33. Referring then to the same units the
velocity V and the radius of curvature />, we shall
have the measure of the centrifugal force expressed
by its ratio to the weight P, or represented by a
weight. For instance, if the velocity of the motion
be 20 miles per hour, or 29*3 feet per second, and
the radius of curvature be 500 feet, the centrifugal
force will be
/ P y ^9*3 1 p
•' 33X500 19 '
that is to say, in this case the centrifugal force will
be 1^ of the weight of the moving body.
It clearly appears that, when the velocity of the
motion and the radius of the curve are known, the
centrifugal force which urges the body out of the
curve is easily found. We now pass on to the cen-
tripetal force produced by the inequality occasioned
in the wheels of the waggon, by virtue of its lateral
deviation.
When two wheels joined invariably together by
526 CHAPTER XVIII.
the same axle, roll on unequal circumferences, or,
in other words, cease to be equal to each other, it
is clear that instead of together forming a cylinder,
they form a rolling cone. If ab and cd (fig 30)
represent the respective diameters of the two wheels,
and the extremities of those diameters be joined by
straight lines, these will meet at a certain point o,
which will be the vertex of the rolling cone formed
by the two wheels ; and the motion of the waggon
borne on the two wheels will be the same as that of
the cone cod.
But when a cone or frustum of cone is laid flat,
or along one of its generative lines, on a horizontal
plane, and it is ui^ed onward by a force applied
at its centre of gravity, suppose at m, it tends to
assume a circular motion round its vertex o ; and if
we wish to prevent it following that curve, and to
make it move straight forward, the force to be over-
come will be a force precisely equal, and contrary to
that which it would be necessary to apply to a body
directed in a straight line, to curve its direction
according to the circumference of the circle described
by the point m round the point o. Now that force
is the centrifugal force in the circle whose radius is
om. Denoting then by / the radius of that circle,
which depends on the difference of diameter of the
two wheels, and preserving the other notations
as above, the centripetal force thus created by the
motion of the cone, will have for its value
P V»
— . —7- .
9 p
OF CURVES. 527
Moreover, putting D' and D'' for the respective
diameters of the two wheels, and e for the width of
the road, or the space which separates the wheels,
it is plain, from the figure, that we have the pro-
portion
whence we derive
'^ 2 ' u- jy '
But on the other hand, if the tire of the wheel is
inclined ^, as has been shown above, every inch of
lateral deviation of the waggon, will produce in the
wheel a difference of radius of \ inch, or a difference
of diameter of f inch. More generally, if ~ express
a
the inclination of the tire of the wheel, a deviation
of the waggon expressed by X will produce in the
wheel a difference of diameter expressed by
2x
— ^^ •
a
So that if D represent the original diameter of the
wheel, and D^ its diminished diameter, corresponding
to the deviation X, we have
a
and similarly, the opposite wheel will receive an
increase of diameter expressed by
528 CHAPTER XVIII.
D''-D=— .
a
But by adding and subtracting these two equations
we have
a
and
D''+D = 2D.
Hence, finally, the centripetal force above, produced
by a given lateral deviation X, is expressed by
P.ra 4X
*V^
g aeJy
Thus, we have the centrifugal force produced in
the waggon by the fact of its motion in the curve,
and the centripetal force produced in the same
waggon by the conical inclination of its wheels.
But it is to be observed, that the former of these
forces is constant for a given train, curve, and
velocity ; whereas the second varies with the lateral
deviation \ of the waggon. As soon then as the
waggon enters the curve, the centrifugal force will
begin to exert its effect; it will drive the train
towards the outer rail ; a certain deviation X will be
produced, and, as its consequence, a centripetal force
which will increase more and more. But since the
centrifugal force is constant, whereas the centripetal
force on the contrary is increasing, and as these two
forces act in contrary directions on the waggon, they
will quickly settle at a point where they will hold
OF CURVES. 529
each other in equilihrium. Then the waggon will
cease to obey the centrifugal force, and will no
longer be driven out of the curve.
The point at which the two forces will be equal is
given by the equation
p V» P V^
or
9
P
9
P
P
9
P
_ P
9
ya 4X
aeD
P =
-Py
or X, =
aeD
A
which gives
As soon as the lateral deviation of the train shall
have attained this point, it is clear that the waggons
will continue their motion without having any ten-
dency to leave the rails, that is to say, not only
without risk of being thrown off the road, but even
without the flange of the wheels being brought into
contact with the outer rail. Besides, since we have
at the same time p = py that is to say, since the
vertex of the fictitious cone, formed by the system
of the two wheels, will coincide with the centre of
the curve, it is evident that the waggon will turn
exactly with that curve without any dragging of one
of the wheels on the rail.
Thus, on all curves on which the waggon may be
sufficiently displaced, the effect of the curve will be
corrected. But in the construction of railways, it is
usual to give but half an inch of play to the wag-
gons, on each side, on the railway ; that is to say,
2 M
530 CHAPTER XVIII.
that during the normal position of the waggon
between the rails, the beginning of the flange of each
wheel is ^ inch from each rail. The greatest value
therefore that can be given to X, without making the
flange of the wheel rub, is ^ inch, or '0417 foot ; and
consequently the utmost curve that can be remedied
by the conical inclination of the wheels, will be
given by the value of p which corresponds to that
maximum deviation, in equation
aeD
Making then this substitution, and replacing at
the same time a, e and D by their ordinary values,
namely, -= y, e = 4*70 feet, and D = 3 feet, we
a
have for the least possible radius of curvature,
p'= 592 feet.
Consequently, it appears that with the conical in-
clination adopted, of \ for the tire of the wheel,
and the play of the waggons ^ inch on the rails on
each side, there may be constructed on railways
curves of 600 feet of radius, without the flange of
the outer wheels of the waggon being exposed to
touch the rails on that side. As, however, this
result supposes the two rails exactly level with
each other, and that there might occur, dining
the work, an accidental depression of the outer
rail, wJhich would expose the flange of the wheel
on that side to rub against the rail, we will, for
greater security, limit the foregoing result to curves
having 1000 feet of radius.
OF CURVES. 531
It must however be added, that there exists, in
the passage of curves, a particular cause of re-
sistance which we have not yet treated of, and
which subsists notwithstanding the conical inclina-
tion of the wheels. It consists in this, that the
two axles of each waggon are parallel to each other,
whereas for the wheels to turn freely along the
curve, like the cone to which we have assimilated
them, the two axles ought to be convergent, on
the side of the centre of the curve, and ought to
concur precisely to that point. But as long as the
question regards only curves of 1000 feet of radius,
this circumstance may very well be neglected. In
effect, the width of the way being 5 feet or -5^ of
the radius of the curve, it is plain that for the axles
to converge to the centre of the curve, their distance
apart, on the side of the inner rail, should be ^^
less than on the side of the outer rail. Now the
distance between the axles in their parallel position
is about 5 feet or 60 inches : the inclination suitable
to them would then be -yj^j^ of 60 inches or 3-tenths
of an inch ; and this smaU quantity is to be divided
into quarters between the four extremities of the
axles, which would make 7-hundredths of an inch
at each of these points. But as so very small a
measure is quite inconsiderable in practice, and
as, besides, the flexibility of the springs on which the
axles are mounted easily yields to so slight a devi-
ation, we deem it perfectly needless to dwell on this
circumstance. Curves therefore of a radius not less
532 CHAPTER XVIII.
than 1000 feet, may without inconvenience be con-
structed on railways.
By augmenting the play of the waggons on the
railway, or the conical inclination of the wheels,
this faculty might be extended to curves of less
radius; but as it might be apprehended that the
result would be a continual rocking of the waggons
during their motion on the straight parts of the
railway, we limit our views here to the determining
of the curvature which is possible in the present
state of things.
Sbct. III. Of the superelevation of the outer rail to
be employed in curves whose curvature is not cor-
rected by the conical inclination of the wheels.
From what has just been seen, if a curve had a
radius of curvature less than 1000 feet, and if
nothing else were changed in the ordinary disposition
of the rails, the flange of the outer wheel might come
in contact with the rail on that side, before the
proper deviation of the wa^on could oppose a suffi-
cient counterweight to the centrifugal force which
produces that motion. The result would be not
only a friction of the flange against the rail, but a
possibility of the train itself being thrown off the
rails. It will therefore be proper to consider what
are the means of preventing that effect.
Now it is evident that by giving, throughout the
curve, a superelevation to the outer rail above the
inner, we shall make the railway form a plane
^
OF CURVES. 533
inclined in the direction of its width. The waggons
placed on this inclined plane must, hy virtue of their
gravity, slide towards the inner rail, which is the
lowest. On the other hand, the centrifugal force
drives them towards the outer rail, which is higher.
We thereby then create a counterpoise to the centri-
fugal force. Thus, by this disposition, we are enabled
to prevent the waggons being thrown off the line.
But it is to be remarked, that since the waggons
may always deviate half an inch laterally, without
the flange of the wheel touching the rail, this de-
viation must first be taken advantage of to balance
a portion of the centrifugal force. It is simply
then the remainder, or the difference between the
centrifugal force and the centripetal force arising
from the greatest deviation of the waggons, that
we need counteract by means of the superelevation
of the outer rail.
If we denote by y the superelevation of the outer
rail above the inner, since e expresses the width of
the way, the inclined plane on which the waggons
are placed, during the passage of the curve, will be
inclined ^; and consequently the gravity of the
waggons will draw them towards the inner rail with
the force
PxL
e
Now it is required that this force, joined to the
centripetal force due to the greatest possible de-
viation of the waggons on the rails, hold the centri-
534 CHAPTER XVIII.
fugal force in equilibrium. Calling then p the radius
of curvature corresponding to the greatest lateral
deviation of the waggons, as was found in the pre-
ceding section, we shall have
P y .P v«_p v«
^ 9 P 9 P
which gives
9 ^P P^
Consequently, substituting for p its value already
found, p-^ 1000 feet, and at the same time re-
placing e and g by their corresponding values,
namely, e = 4*70 feet and ^ = 33 feet, it is plain
that, for every curve, it will be easy to determine
the superelevation to be given to the outer rail, to
counterbalance the centrifugal force, and to displace
the waggon as much as may be possible, without
however making the flange of the outer wheel rub
against the rail.
It must however be added here, that as the
necessary superelevation, or the value of y, in-
creases in the ratio of the square of the velocity
of the motion, it is indispensable to calculate y,
not for the average velocity of the motion, but
for the greatest velocity the trains can acquire.
Otherwise the superelevation of the rail would no
longer suffice for cases of very great velocity, and
accidents might happen in the curves.
Performing the calculation for difierent velocities,
and for a railway 5 feet wide, we obtain the follow-
ing results :
OF CURVES.
535
Table of the superelevation to be given to the outer rail in
curves.
Designation of the wsggons
. and the wmy.
Radius
of the
curre.
Sap^rderation to he giren to the outer rail,
in inches, the maximum relodty of the
motion, in miles per hour, being :
90 miles. SO miles.
40 miles.
50 miles.
60 miles.
Waggon with wheels 3 feet
in diameter.
Width of way, 4^70 feet
Play of waggons, on the rail-
way, on each side, '5 inch.
Inclination of the tire of the
wheel, |.
feet.
900
800
. 700
600
500
inches.
•16
•37
•63
•98
1^47
inches.
•37
•83
1^42
2-21
3-31
inches.
•65
1-47
2^52
3*92
ft
inches.
102
2-30
3-94
tt
tt
inches.
1-47
3-31
ft
tt
tt
When the outer rail of a curve has this super-
elevation, it is clear that, if a train of waggons
traverse the curve at the maximum velocity for
which the superelevation has been calculated, the
train will deviate laterally as far as the rise of the
flange of the wheel, and will continue its motion
in that position to the end of the curve, since the
divers forces then applied to the waggon, either to
drive it outwards, or to bring it back within the
curve, will hold each other in equilibrium. There
will be no risk of accident then to fear ; but the
resistance of the train will be greater than on a
railway in a straight line. In effect, the curve
traversed will have a radius expressed by p, and
the rolling cone, formed by the conical inclination
of the wheels, will have the radius p\ which is
greater. For the cone to roll of itself along the
curve, making the wheels describe distances, un-
equal in the same proportion as the lengths of the
outer and inner rails, it would be necessary, as has
536 CHAPTER XVIII.
been seen above, that p should be equal to p. The
dragging of the wheels will therefore take place on
the difference between the circumferences described
with the radii p and p. The parallelism of the
axles, besides, will have an effect by so much the
greater as the radius of the curve is smaller. The
superelevation of the rail, such as we have deter-
mined it above, is then to be considered as rendering
impossible, in the regular state of things, that the
train should be thrown off the rails, and not as
destroying all increase of resistance in the passage
of curves. Some ingenious means have been pro-
posed to attain this latter result, but as they are not
yet sufficiently confirmed by experience, we refer
the reader to the publications in which their in-
ventors have developed the advantages to be de-
rived from them.
We will however observe that, in general, the
only object of all the modes proposed for passing
curves, is to obviate the inconveniences which they
offer in the normal state of things. But a rail
broken or accidentally raised, a stone fallen on the
road, an axle or a wheel broken, always present
chances of much more serious accidents on curves
than on the straight Une.
APPENDIX.
EXPENSES OF HAULAGE BY LOCOMOTIVE ENGINES
ON RAILWAYS.
To complete the knowledge of locomotive engines, it still
remains to consider them with regard to their economy ;
that is to say, to examine the amount of the expenses
attending the haidage by means of locomotive engines
on railways. This research will be the object of the
present Appendix.
We shall draw the documents we have to present on
that subject from the two most ancient enterprises of the
kind in England : the Liverpool and Manchester, and the
Stockton and Darlington Railways. They will have, be-
sides, the advantage of presenting examples of two very
different sorts of conveyance: the one rapid, and prin-
cipally composed of passengers; the other slow, and
consisting of goods.
We shall divide the expenses incident to locomotive
engines on railways in the following manner :
The repairing and maintaining of the 'engines, their
consumption of fuel, and the expenses for conducting
them, constituting together the expenses for locomotive
power, properly so called ;
The expenses for the maintenance of the way;
The office expenses and contingencies, which, united
2n
538 APPENDIX.
with the preceding, give the total expense of the haulage
by means of locomotive engines on railways ;
Finally, we shall conclude with a glance at the receipts
compared with the expenses, which will show the profits
arising from these enterprises, to the companies who
carry them into execution.
In treating of these various subjects, througliout this
Appendix, we shall ^ve the amount of expenses per ton
gross, that is, including the weight of the waggon which
conveys the goods. This is the most accurate method,
since it refers to the effort really exerted by the engines,
and to the weight effectively borne by the rails; and it
matters little, as regards the engine or the rails^ whether
in this total weight, a half merely or any other proportion
be composed of merchandise or useful weight. It will
afterwards be easy, on any line of road, to deduce the
cost of conveyance per ton 0/ goods, when once, on that
line, knowledge is obtained of the weight of the waggon
compared with that of the load. In the weight of a
loaded waggon, generally, the load is two-thirds, the
waggon one-third, which establishes at |- the ratio of the
effective tons, or tons of useful weight, to the tons gross.
Sect. I. Ejcpense /or repairs 0/ locomotive engines.
Among the expenses just enumerated, that which will
naturally first engage our attention is the expense for
keeping the engines in repair.
Before we enter into any calculations on tiiat head, it is
necessary to mention that what is meant by repairs to the
engines, is nothing less than their complete re-construc-
tion; that is to say, when an engine goes into repair,
unless it be for some trifling accident, it is taken to pieces
and a new one is constructed, which receives the same
name as the first, and in the construction of which are
EXPENSE FOR REPAIRS OF ENGINES. 539
made to serve all such parts of the old engine as are still
capable of being used with advantage. The consequence
of this is^ that a re-constructed or repaired engine is
literally a new one. The repairs amount thus to con-
siderable sums^ but they include to a great extent the
renewal of the engines.
According to the Tables at the end of this work^ it will
' be seen that in the year ending on the 30th of June, 1834^
the repairs of the engines of the Liverpool Railway cost —
From June 30, to December 31, 1833.
Materials for repairs .... £ 3.755 3 7
Workmen 4,401 4 10
Repairs out of the establishment 613 3 9
£8,769 12 2
From December 31, 1833, to June 30, 1834.
Materials £4,140 19 6
Workmen 5,-432 8 8
: 9.573 8 2
£18,343 0 4
The question is now what was the work executed by
those engines during that interval ? Now, referring to the
same Tables which will be found below, it will be seen
that the goods conveyed on the line during the year
were —
Between Liverpool and Manchester 139,328 1.
On part of the hne, making an average of 15 miles,^
24,934 1., which, on the whole, is equal to . . . 12,467
Total . . . 151,795 1.
In the Tables just mentioned, there appears indeed
some other haulage executed, such as goods for Bolton
^ The distance to which the Company carries the Wigan and
Warrington goods, which form the principal part of this article, is
15 miles.
540 APPENDIX.
and coal for several places along the line ; but this work
is done by engines which do not belong to the Company^
so that their repairs are not included in the following
reports^ and for that reason we do not take it into account
in this place.
The above weight is that of the goods conveyed^ to
which must be added the weight of the waggons. Now, on
that railway, the average load carried on a waggon is 3*5 1.,
and the waggon itself weighs 1*5 t. ; so the weight of the
carriages that served for the above-mentioned tonnage will
be known by multiplying the number obtained^ by the
1*5 . r
ratio ---. And as, moreover, the engines, for want of
suf&cient returning traffic, are obliged to. bring back half
the waggons empty in one of the two directions, or i of
the whole, we shall have for the gross weight drawn by the
engines in the course of the year —
Weight of the goods 151,795 1.
Weight of the corresponding waggons .... 65,055
Weight of the waggons brought back empty . . 1 6,264
233,1 14 1.
This is the tonnage of the goods, to which must be
added that of the travellers. In the course of the year,
415,747 travellers were conveyed from one city to the
other in 6570 trips.* This makes an average of 64
travellers per train. The coaches required for that num-
ber of travellers, including the empty carriages added to
each train to-be ready for any emergency, are six carriages
of the first class, or five of the second.'
' Tliia is the number of the travellers inscribed in the Com-
pany's books. It includes neither the travellers put down nor
those taken up on the road, the numbers of which balance each
other.
' The first-class carriages are glass coaches, containing each 13
EXPENSE FOR REPAIRS OF ENGINES. 541
The weight of six first-daas coaches, indading the mail, is 21 t.
The weight of a second-class train of five carriages, in-
dading one glass coach, is 12*6
Lastly, for 13 trains of the first class there are 16 of
the second. Thus, the average weight of the carriages for
every 64 travellers may be reckoned at 16*4 1.
Consequently, the gross weight corresponding to the
travellers conveyed was —
415,747 travellers, at 15 per t 27,717 1.
Corresponding weight of the carriages .... 107,748
Luggage of the travellers, at 28 lbs. each . . . 5,197
140,662 1.
Thus the total weight drawn during the year, by the
engines belonging to the Company, was —
Gross weight for goods 233,1 14 1.
Gross weight for travellers 140,662
373,776 1.
Now we have already shown in this work (Chap. XVII.
Sect. VI.) that, taking into account the siirplus of resistance
caused by the gravity of the train and the engines, on
the different inclines of the Liverpool and Manchester
Railway, the quantity of work executed in the traction of
any load, over the whole extent of the line, may easily be
determined by the following expressions :
From Liverpool to Manchester . . W. = 30*79 M, 4- 262,
From Manchester to Liverpool . .*W. = 36*89 M, + 348,
in which W figures for the quantity of work executed,
expressed in tons groiA drawn one mile on a levels M , the
persons ; they weigh 3*65 1. Those of the second dass are open,
and have 24 places; their weight is 2*23 1. Lastly, the mail-
coaches weigh 2*71 1., and carry 10 travellers. Each glass coach
has besides one outside place.
542 APPENDIX.
load of the engine, in tons gross estdmmm oftemdery and
the numbers 262 and 348 the average woik canaed by the
gravity of the engines and their tender, and by the traction
of that tender. Taking dien a mean between these two
expresnons, it will appear that the oonTeyanoe of a load
M, finom one end erf the line to the other, in both direc-
tions, will produce a q[iiantity of woik expressed by
W.=3d-84M. +305 tons gross 1 mile on a levd«
This premised, as the above 373,77^ tons gross were
conveyed by the engines in 11,656 trips, it follows that
die average load of the engines per trip was 32 tons gross.
Substitnting then this number for M, in the preceding
expression^ we find duit the work done by the engines in
each trip was 1387*9 tons gross drawn 1 mile an a ieveL
Thns as the engines performed in aD 11,656 trips, the total
work done by them was
11656x1387*9= 16,177,080 tons gross drawn 1 mile on a level;
and the ratio of this number to the real conveyance
effected, namely, 373,776 tons gross drawn 29*5 miles,
or 11^026,392 tons gross drawn 1 mile, shows at the same
time that, on that line, the gravity and draught of the
tendera increase the work of tiie engines in the |Hroportion
of 1-467 to 1.
For the work above stated, the repaira of the engines
cost £ 18,343 0». 4d. This smn, reduced to pence, gives
4,402,324 d. Consequently the repaira, per ton.gross con-
veyed 1 mile on a level, amounted to
4402324^
15177080
=•272^.
To perform this work, tiie engines made 6570 trips
with travellers, that is to say, at a velocity of 20 miles per
hour; and 5086 trips, with goods, or at a velocity of 12-5
miles an hour. The average velocity of the haulage was
therefore 16*73 miles per hour.
EXPENSE FOR REPAIRS OF ENGINES. 543
We have said elsewhere that, at the time of these ob-
servations, the Liverpool and Manchester Railway Com-
pany possessed thirty locomotive engines. It must not
be concluded, however, that that number is necessary in
order to perform the above-mentioned haulage. Of these
30 engines, about one-third were useless. This third
consisted of the most ancient which, having been con-
structed at. the first establishment of the railway, at a
time when the Company had not yet obtained sufficient
experience in that respect, are found now to be out of
proportion with the work required of them. The engines
in daily activity on the road "amounted to about 10 or 11,
and with an equal number in repair or in reserve, the
business might have been completely ensured; for the
surplus, above that number, was nearly abandoned.
We shall complete what has just been smd on the
Liverpool and Manchester locomotive engines, by adding
a document that will show what these engines are capable
of executing in a daily work, and the improvement they
have undergone in the course of the last few years, with
respect to their construction.
544
APPENDIX.
Work done by the ten best locomotive engines of the lAver-
pool and Manchester Railway, during the years 1831,
1832^ 1833^ and the first twelve weeks 0^1834.
Year.
Name of the engine.
Total time
the engine
has been on
the road,
either in
activity or
in repair.
Total
travelled by
the engine.
1831.
Mkrcurt
JUPITBR
Planbt
Saturn
Mars
Majbstic
North Star ....
Northumbrian . . .
Phcbnix
Sun
Total
Ayerage per week
Weeks.
52
44
52
38
50
52
52
52
52
37
481
Blika.
23,212
22.528
20,404
19,510
18,645
18,253
15,677
15,607
15,405
13,434
182,675
380
1832.
Vulcan
LiVBR
Vbnus
Etna
Saturn
Vbsta
Victory
Planbt
Sun
Fury
Total
Average per week
52
43
52
52
52
52
52
52
52
52
511
26,053
22,651
20,464
20.399
20,312
17.739
17,082
16,885
16,5«5
15.603
193,723
379
EXPENSE* FOR REPAIRS OF ENGINES.
545
Work done by the ten best locomotive engines of the lAver^
pool and Manchester Railway, during the years 1831^
1832^ 1833^ and the first twelve weeks of 1834.
Year.
1833.
Name of the engine.
JUPITBR
Ajax
FiRBPLT
LiVBR
Pluto
Vesta
Lbbds
Saturn
Vbnus
Etna
Total
Average per week . .
Total time
the engine
has heen on
the road,
either in
activity or
in repair.
Weeks.
52
52
39
52
52
52
48
52
52
52
503
Total distance
travelled hy
the engine.
Miles.
31,582
26,163
24,879
23,134
20,308
19,838
19,364
18,738
18.348
17,763
220,117
438
1834.
FlRBVLT
Vulcan
Saturn
Liter
Sun
Etna
Leeds
Ajax \
Venus
Pluto
Total
Average per week
12
12
12
12
12
12
12
12
12
12
120
8,542
8,526
7,290
7,080
7.080
6,557
5,712
4,890
4,632
4,246
64,555
538
546 APPENDIX.
As we have already said that the average load of the
engines, on this railway, is 32 tons gross^ exclusive of
tender y it would be easy to deduce firom this Table, the
number of tons gross which have been carried 1 mile by
each of the engines during the time of its work. Similarly,
by dividing the number of miles travelled by the length
of the railway, which is 29*5 miles, we might dedace firsts
the number of trips performed by each engine ; and then,
recollecting that each trip, with the average load of 32
tons gross, corresponds to 1388 tons gross drawn 1 mpe
on a level (page 542), we might deduce the number of
tons gross drawn 1 mile on a level by the engine, either
in the course of a year, or during the whole time it was
on the line. We will not offer this calculation for each
engine, but will ^ve the result of it for those two^ among
them, which have done the most work.
At the time of the completion of the above Table^ the
Liver had been employed on the railway during 107
weeks, had travelled a distance of 52,865 miles, or drawn
2,487^140 tons gross, tender included, one mile on a level;
the Firefly had worked 57 weeks, had travelled a distance
of 33,421 miles, or drawn 1,572,360 tons, gross, tender
included, one mile on a level; the average velocity at
which these loads had been, drawn was 16*73 miles per
hour, and neither of these engines, at the period in
question, had yet required a thorough repair.^
To give an example of the expense of repairs of lo-
comotive engines, under other circumstances, and with
engines of another construction, we will here set down
the work performed by the locomotive engines on the
K
^ The greater part of these excellent engines were built by
Mr. R. Stephenson. The Liver engine is the work of Mr. Edward
Bury, of Liverpool.
EXPENSE FOR REPAIRS OF ENGINES. 547
Stockton and Darlington Railway, during the same year,
that is to say, from Jmie SO, 1833, to June SO, 1834, and
the amount of expenses for repairing those engines during
the same space of time.
On this railway, the engines performed, in the course
of the year, and descending with their loads, a number of
trips which, estimated in trips of 20 miles each, according
to the custom of the Company, amounts to 5318*5, or
5119 trips^of 20*78 miles each; and this necessarily
carries with it an equal number of trips in ascending
with the empty waggons. The load of the engines at
each trip going down, is 24 waggons, carrying 63*6 tons
effective of coal, and weighing in tons gross 94*8 tons.
In bringing the 24 empty waggons up again, the load of
the engines is 31*2 tons gross. Recurring to the expres-
sion which we have given Sect. vi. Chapter XYII., of
the work done in conveying a given load on the whole
extent of this railway, it will readily be perceived that,
considering the bringing back of the waggons empty,
every trip descending corresponds to the draught of 2650
tons gross 1 mile on a level; and consequently the total
work exiecuted in the year on this railway, amounts to
13,565,350 tons gross, one mile on a level.
With regard to the corresponding expenses, it is to be
noted that, after having for a long while kept and re-
paired their engines themselves, the Directors of the
Stockton and Darlington Company decided, in order to
avoid minute accoimtd, to do all that work by contract ;
and, in consequence, in 1833, they put their engines into
the hands of three persons. By the contract entered
into, the Company paid ^V of a penny per ton of goods
carried one mile; and, for that price, the contractors
undertook, not only to keep the engines in good repair,
furnishing workmen and materials, but also to pay all the
current expenses of haulage, such as salary of the engine-
548 APPENDIX.
men^ fuel^ oil, grease, &c.; and to pay moreover to the
Company an interest of five per cent, on the capital
representing the value of the engines, and of all die
establishments placed at the contractors' disposal for their
work.
The total sum paid to the contractors by the Company
for that object during the year ending June 30, 1834^
was
£11,347 Is. 9<^.;
and deducting the expenses for rent, interest of capital
and haulage, the amount of which is known, the Directors
of the Company reckon that the definitive sum remaining
with the contractors for the repairs of the engines (bars
of fire-box included), amount, with the general profit on
the whole bargain, to
£5,732 18«. 5d.
This sum, reduced to pence, gives
1, 375,901 e^.
It was expended for the carriage of 13,565,350 tons gross
one mile on a level ; so that finally the expense, per ton
gross carried one mile on a level, including the profits on
the bargain, amount to
OlOlrf. ,
As a complement to what we have said, and to show,
on this railway as well as upon the Liverpool one, the
work the engines are able to perform, we shall, give a
Table of the haulage executed, and repairs done to the
engines, during five months of the year 1833.
To form, in this Table, the column which contain^ the
work done, in tons gross carried 1 mile on a level, tender
included, the number of tons of coal carried 1 mile
descending is multiplied by 2; because, from the cal-
culation indicated page 547^ the conveyance of a load of
63*6 tons of coke, along the whole line, or the distance of
EXPENSE FOR REPAIRS OF ENGINES. 549
20*78 miles, corresponds, including the return of the
empty waggons, the gravity, &c., to a quantity of work
expressed by 2650 tons gross drawn 1 mile on a level;
and that this number is double the product 63*6 x 20* 7B
= 1322, which represents the useful work done at each
trip, or the number of tons of coal carried 1 mile by
the engine.
The last column but one of the Table contains the
amount of expenses for keeping each engine in repair
during the time it was on the line, and the last column
contains the same expenses divided per ton gross drawn
1 mile on a level; but we must add that, at the time
when this Table was formed, there were, among the
engines of the railway, twelve completely new. Besides,
the amount of repairs here set down includes only the
workmen^s wages, and not the materials, those materials
having been purchased largely and kept in store. It is
therefore subjected to these restrictions, that we present
the foUowing Table.
Most of the engines of the Stockton and Darlington
Railway were built by Mr. T. Hackworth, of Brusselton,
near Darlington.
550
APPENDIX.
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EXPENSE OF FUEL. 551
Sect. II. Ewpenae of Fuel.
We have already, in Chapter IX. of this work, related
experiments from which may be deduced the consumption
of fuel according to the load the engines have to draw.
However, as in the intervals of the trips, the fire must be
kept up, and as, besides, there are always imavoidable
losses during the work, an increase of expense in that
respect must naturally be expected in practice. This we
also learn in a positive manner by the examination of
facts.
According to the half-yearly reports of the Liverpool
Railway Company, for the year ending June 30, 1834,
the expense for fuel for the locomotive engines was
£6,079 15«. Se^.
The number of trips performed was 11,656: conse-
quently the expense for fuel for each journey amounted to
10*432^.; and as the average price of coke used during
that year on the railway was 23*5^., the consumption of
fuel, measured in weight, amounted to 994*37 ffis. per
trip. Now we have already seen that the average load of
the engines, during the year, was 32 tons gross. A load
of 32 tons, not including the tender, consequently re-
quired, by the fact, a consumption of coke of 994lbs.
Thus, as the work corresponding to the conveyance of
that load from one end of the line to the other is equi-
valent to 1388 tons gross carried 1 mile on a level (page
542), it is plain that the consumption of fuel amounted to
'7161b. of coke per ton gross carried 1 mile on a level ;
and from the price of coke on that line, that consiunption
cost
'090<f. per ton- gross carried 1 mile on a level.
Our special Experiments given Chapter XL. only give
an average consimiption of 784lbs. of coke for a load of
552 APPENDIX.
32 tona» By this it will be seen that, in practice^ and
with the nature of the business on that line, the different
losses amount to one-fourth of the expense of the active
work. This considerable increase is owing not only to
the necessary expense for lighting the fire every morning,
bat also to the necessity, on that Une, of keeping, for the
passage of the inclined planes, helping engines, the fixe of
which must remain alight the whole day, although they
only serve at distant intervals; to the number of trips
which the engines make almost without load ; and in fine,
to the long delays between one journey and another.
These circumstances, that of the helping engines alone
excepted, are inevitable in a business of the nature of
that of the Liverpool and Manchester Railway*
On the Stockton and Darlington Railway the same
causes of loss do not exist, at least not to the same
d^ree.
According to the notes, carefully kept by the Directors
of that Company to serve as a foundation to the contracts
they sign, the quantity of coal consumed on an average,
during one journey of an engine, that ia to say, to convey
24 loaded waggons a distance of 20 miles down lull, and
bring them back again empty to the same distance up
hill^ costs the engine-men 4«. 9}i/., when the coals are at
5s. per ton. So the weight of coals consumed is 21571bs.
Now we have seen that the work done in one trip is
equivalent to 2650 tons gross drawn 1 mile on a level;
the consmnption of coal per ton gross carried 1 mile on a
level is therefore
•814ft..
or, from the price of the fuel,
•0218J.
This is. nearly the same consumption in weight as. on
the Liverpool and Manchester Railway. The result may
EXPENSE OF LOCOMOTIVE POWER. 553
appear surprising ; for the boilers of the Darlington engines
are generally constructed on a less economical principle,
as to the application of heat, than the Liverpool ones ; but
considering the work of each line, this circumstance will
easily be accounted for. On the Darlington Railway the
engines never go off but with a full load ; that is to say,
that, taking the two trips together, the descending and the
ascending, the engines draw, as has been shown, an
average load of 63 tons gross per trip, which circum-
stance we know to be favourable to the expenditure of
fuel. If these engines drew only an average load of 32
tons, like the Liverpool ones, their relative consumption
would certainly be greater. To this must also be added
that, on the Darlington Railway, the engines suffer no
delay between their trips.
It is to these combined circumstances that the practical
result appearing in this case must be attributed. As
railways for goods are generally found to have these
advantages over railways for travellers ; that is to say, as
less frequent departures admit of starting the engines
more completely loaded and with less loss of time between
the trips, it ought to be consiidered that the comparative
saving of fuel which we notice, originates in the very
nature of the work itself.
Sect. III. Eoepense of locomotive power.
To the expenses just noted, ilamely, the repairs of the
engines and the fuel, are to be joined several accessory
charges for the conducting of the engines, such as engine-
men^s and assistants' wages, oil,. grease, hemp, &c. The
amount of these divers objects taken in their detail, is
reported in the Tables of receipts and expenses of the
Liverpool and Manchester Railway, which will be given
2 o
554 APPENDIX.
farther on ; but it is necessary to consider them here taken
collectively.
These charges, together with the expenses for repairs
of the engines and the expenses for fuel, constitute the
expenses of locomotive power, properly so called. It is
then indispensable to include them in the calculation, in
order to know the definitive cost of locomotive engines
used as a means of conveyance.
It will be seen in the Tables of detail given farther on,
that on the Liverpool and Manchester Railway the ex-
penses of locomotive power amounted, during the year
under consideration, to the sum of
£29,607 53. lid.
As we have seen that the work done by the engines
amounted to 16,1779080 tons gross, drawn one mile
(page 542), it follows that the expenses for locomotive
power, were
'4S9d» per ton gross per mile on a level, at an average velocity
of 16*73 miles per hour.
On the Stockton and Darlington Railway, we have said
that the Company passed a contract for the locomotive
power, and that the total price paid to the contractors
during the year was
£11,347 U. 9d.
Out of this sum the contractors pay to the Company, for
rent of work-shops, and interest of capital vested in
engines,
£824.
There remains, then, definitively paid for locomotive
power,
£10,523 Is, 9d.i
and as this sum has defrayed the conveyance of 13,565,350
tons gross to 1 mUe (page 547), the rate of that expense was
EXPENSE FOR MAINTENANCE OF WAY. 555
'186 if. per ton gross per mile on a level, at the speed of 8 miles
per hour.
This expense^ however^ refers to coal used as fuel. As
this circumstance does not occur on the railways recently
formed^ and particularly on the Liverpool and Manchester
Railway^ it will be necessary^ in order to have prices com-
parable between them^ to take into account the difference
of price of the two fuels.
Now, the Darlington Company bum •814115. of coal
per ton gross per mile on a level. Supposing in the two
kinds of fuel an equal power of producing heat, the con-
sumption of coke would also be *8141l3., and taking that
fuel at the Liverpool price, namely, at 23s. Gd. per ton,
the expense per ton gross conveyed one mile would be
'I02d., instead of *022«f., which it actually is. There
would then be an augmentation of expense per ton gross,
per mile, of
OSOd,
Thus, with the use of coke instead of coal on the
Stockton and Darlington Railway, the expense for loco-
motive power would amount in this year to
'2S6d. per ton gross per mile on a level, at the average velocity
of 8 miles per hour.
It will be remarked that this expense, compared with
that of the Liverpool and Manchester Railway, for the
same object, is within a very little in proportion to the
velocity on each line, namely, 8 miles per hour in one
case, and about 17 miles per hour in the other: this is a
point which we shall again touch upon farther on.
Sect. IV. Expense for maintenance of way.
The expenses for keeping the Liverpool and Man-
chester Railway in repair, during the year under con-
556 APPENDIX.
sideration^ from June 30^ 1833^ to June 30, 1834, were^
according to the Tables of detail given hereafter,
£15,776 128. Id.
During the same time the following weights passed on
the railway, drawn either by the Company's engines, or
by engines belonging to other companies, namely :
OoodB on the whole road 139,328 /.
on half the road 24,934 tons, making on the
whole road 12,467
between Bolton, and Manchester or Liver-
pool, 38,341 tons, or on the whole road . . 19,170
Coal on half the line 86,173 tons, or on the whole . 43,086
1*6
Conresponding waggoni, 1- of the weight of the goods 128,431
3*5
Waggons brought back empty, J^ of the whole • 32,108
Total for goods and coal 374,590 t.
Coaches, trayellers, and luggage, as above . 140,662
515,252 t.
Thus 515,252 tons gross passed over every mile of the
railway, exclusive of the weight of the engines and their
tender. The expenses for maintenance of way having
been j£ 15,776 12^. Id. for 31 miles, the whole length of
the railway, or j£508 ISs. Sd, per mile, they amount to
*237<f. per ton gross per mile.
On the Stockton and Darlington Railway, during the
same year, the expenditure for repairs of the road was as
follows :
£ 8. d.
Workmen's wages for repairs to the railway . . 5,320 5 0
Materials for ditto 2,578 3 8
Repairs to bridges 69 17 7
Repairs to walls and fences 280 7 11
Contingendes 467 3 7
8,715 17 9
i
EXPENSE FOR MAINTENANCE OF WAY. 557
And deducting the chaises relative to walls and fences^
which are not included in the preceding article for the
Liverpool and Manchester Railway, as may be seen in the
detailed accounts presented further on, the amount of this
expenditure reduces itself to
£8,435 98. \0d.
On the other hand, the weights which passed on the
railway, drawn either by locomotives or by the stationary
engines or by horses, wei'e :
ton* to 1 mile.
375,320 tons of coal, equal in tons carried one mile, to 8,526,904 t.^
32,996 tons of Ume-stone 133,064 18,858,193
17,387 tons of goods 198,225 J
6,499 tons in passengers, equal to 53,733
1*30
Waggons, of the weight of the goods conveyed . 4,345,529
2*65
Waggons brought back empty, same weight 4,345,529
Weight of coaches, in tons carried one mile 161,199
Total 17,764,183/.
The expense per ton gross per mile, exclusive of the
weight of engine and tender, amounts then to
*1 14(/. per ton gross per mile.
Taking the repairs of walls and fences into the account,
this article would give *118i/. per ton gross per mile.
It must be observed that this expense, as well as that
above mentioned for the Liverpool and Manchester Rail-
way, is rather higher than it will be on an average for the
years to come, on account of an extraordinary replacing of
the rails of both lines, by other rails of much greater
strength.
The expenses for keeping in repair the Stockton and
Darlington Railway would unquestionably be less, if the
waggons used on that line were on springs, like those of
the Liverpool and Manchester Railway. In the present
state of things, however, those expenses scarcely amount
to half the expenditure of the Liverpool and Manchester
558 APPENDIX.
Railway for the same object ; that is to say^ they are, as
well as the expenses for locomotive power, very nearly in
proportion to the velocity on each line.
It must not however be thought that the great differ-
ence observed in this respect between the two railways^
is exclusively owing to the velocity of the motion. That
velocity, indeed, constitutes much of it, but the conditions
attending each sort of business have a no less consider-
able influence. What we mean is, that the conveyance
of passengers forming the chief business on iixe Liverpool
and Manchester Railway, their safety requires that much
more care be taken of the engines than when the load is
composed only of coal, as on the Stockton and Darlington
Railway. The consequence is, that the Liverpool engines
are kept with a degree of care, we might even say of
luxury, to which the Darlington ones can by no means
be compared. To explain our idea completely, we may
say that the business of the Darlington Railway is a
business of waggonage, and that of the Liverpool Railway
a business of stage coaches.
The data laid down above must therefore be taken each
in their speciality, that is to say, the one as suitable to a
slow motion, with engines of a certain construction and
intended for the draught of goods, and the other to a
rapid motion with engines of a different construction, and
intended for the draught of passengers, for which the
former would be unfit.
Before we close this article, we must remark that the
repairs of the railway consist principally in replacing the
blocks, chairs, keys, and pins. The rails themselves, being
of malleable iron, seldom break. As for their gradual
decrease of weight, by wear, that is a very inconsiderable
effect, as may be seen by the following fact.
On May 10th, 1831, on the Liverpool and Manchester
Railway, a malleable iron rail, 15 feet long, carefully
cleaned, weighed I7711^s. 10^ oz. On February 10th, 1833,
TOTAL EXPBNSB OF HAULAGE. 559
the same rail, taken up by Mr. J« Locke, then resident
engineer on the line, and well cleaned as before, weighed
176113s. 8 oz. It had consequently lost in 21 months a
weight of 18^ oz. The number of tons gross that had
passed on the rail during that time was estimated at
600,000. Thus we see that with so considerable a tonnage,
and with the velocity of the motion on that railway, the
annual loss of the rail was only -^-f^ of its primitive
weight. So that it would require more than a hundred
years to reduce it to the half of its present strength*
Sect. V. Total expense of haulage.
So far we have seen to what rate per mile the expenses
amoimt for locomotive power and for maintenance of
road. But to determine the definitive rate of the expenses
of all kinds, necessary for working raUways by means of
locomotive engines, it still remains to make the same cal-
culation for each of the other expenses incident to these
engines on the railway.
Taking each of these charges from the detailed Tables of
the Liverpool and Manchester Railway Company, and
dividing it according to the respective work to which each
refers, we arrive at the following result : —
r
560
APPENDIX.
Partition of the expenses of haulage on the Liverpool and
Manchester Railway.
Expense per ton
gross per mile.
£, 8, d,
15,971 13 6
25.270 7 1
10,686
10
4
29,607
5
11
15,776
12
1
2,294
6
8
3,462 15 5
13,373 6 8
116,442 17 8
TnTellen.
ft
u
Repairs to coaches, compeiisation for lug-
gage lost, offices for booking passen-
gers ; to be divided according to a gross
tonnage, for travellers, of 140,662 tons
(page 541) and for a length of road of
30 miles, makes '90837^
Loading of goods, compensation for ditto,
cartage in the towns of Liverpool and
Manchester, loading and miloading of
coals; to be divided according to
374,590 tons gross of goods and coals
(page 556) and for 31 miles of road,
makes
Interest on borrowed capital
Locomotive power already divided (on
the level) -43925
Maintenance of way already divided .... '23705
Stationary engine and tunnels ; to be di-
vided according to 515,252 tons gross
(page 556) and for 31 miles, makes per
ton gross per mile '03447
Repairs to waggons; to be divided ac-
cording to 233,114 tons gross drawn
to 31 miles (page 540) makes „
Direction, offices, engineers, law expenses,
police, rent, taxes, rates, repairs to
vralls and fences, and petty expenses; to
divide (page 541) according to 373,776
tons gross and for 31 miles, makes . . '27700
Goods.
»»
•52235'
f»
•43925
•23705
Total per ton gross per mile on a level 1*89614^
And consequently :
Total expense per traveller per mile on a
level, (page 541) 1-89614 x 4f§jff . . -64153
Total expense per ^eelwe ton of goods
per mile on a level, (page 540)
162512 X ^
3'5
ir
•03447
11500
-27700
1-62512'
232160
TOTAL EXPENSE OF HAULAGE. 561
Though each of these expenses is here divided in
proportion to the tonnage and to the length of the road^
it is understood that there are several among them which
would suffer no change^ were the road longer or shorter.
Such are the charges for loadings cartage^ offices^ &c.
Account then should be taken of this circumstance^ were
it desired to deduce from the data of the Liverpool and
Manchester Railway^ what would be the expenditure on a
different line.
According to what has abeady been said of the effects
of the velocity on the repairs of the engines and main-
tenance of the road (Sect. iii. and iv. of the Appendix)^
it may be observed that the trains of waggons^ moving
slower than those of coaches^ ought not^ at equal weights^
to cause the same wear and tear of the engines^ nor the
same repairs to the road. As experience seems to indi-
cate that these effects are^ for an equal tonnage^ in direct
proportion to the velocity^ we shall here take account of
this circumstance by separating first the expenses for
locomotive power and maintenance of way^ each into two
portions^ in the ratio of the tonnage and of the velocity
on each of the two railways ; and it will not be till after
this first partition^ that we shall perform the division of
each portion per ton per mile, as above. This calculation
gives the following results : —
562
APPENDIX.
Partition of the eaipenaes of haulage on the Liverpool and
Manchester Railway, taking into account the difference of
velocity of the trains.
Expense per ton
gross per mile.
TVavellcn.
Locomotiye power: £29,607 5«. lid,, divided on a ton-
nage of 140,662 tons gross drawn at the Telo-
city of 20 miles an hour, for the travellers, on one
part; — and 233,114 tons gross of goods drawn
at the velocity of 12*5 mUes per hoor, on the
other part (pages 540 and 541) ; — ^makes :
For travellers £14,543 7«. lid., or per ton
gross per mile, on a letfel (page 542) '57334'
And for goods £15,063 ISt. Qd., or per ton
gross per mile, on a level (page 542)
Goods.
ff
Maintenance of way: £15,776 12t. Id., divided on a
tonnage of 140,662 tons gross drawn at the ve-
locity of 20 miles an hour for the travellers,
on one part ; — and 374,590 tons gross of goods
drawn at the velocity of 12*5 miles per hour, on
the other part (page 556) ; — ^makes :
For travellers £ 5,921 5«. Id., or -33676
For goods £ 9,855 7«. 0<;., or
Cartage and expenses of all kinds, above specified, and
divided (page 560) 1*21984
Total per ton gross per mile on a level 2*12994'
And consequently :
Total expense per traveller per mile on a level
(see preceding Table, page 560) ^
Total expense per effective ton of goods per mile
on a level (see preceding Table)
-72063
•35834*
ft
•20369
•94882
1-51085'
It
2*15830
TOTAL EXPENSE OF HAULAOE. 563
With these results^ an exact account may now be
rendered of the profits arising from each kind of business.
In effect, the gross receipt, for travellers, during the year,
was
£105,456 38. lOd.,
and the number of passengers conveyed from one end of
the line to the other, a total distance of 30 miles, for the
passengers, was 415,747. Thus the receipt per passenger
per mile is
2029 rf.
We have just seen that the Company disburses for the
same conveyance per mile, on a level, *7206rf.; and dividing
the disbursement per current mile of the railway, (not on
a level,) there would result, for this expense,
•807 rf.
The net profit per passenger per current mile is there-
fore
l-222rf.
Again, taking the goods separately, the receipt for them
is found to be
£81,045 6^. U.;
and as the work done is 151,795 effective tons carried the
distance of 31 miles, as far as the port, the gross receipt
per ton of goods per mile was
4-153cf.:
deducting, for the expenditure per current mile, relative to
the same article,
2-385 cf.,
there remains a net profit, per ton of goods per current
mile, of
l-768rf.
We here see that, when the engines draw an effective
ton composed of 15 passengers, they yield a net profit of
564 APPENDIX.
1 8*330 e(.; and that^ in drawing the same weight of goods^
the net resulting profit is but l*768rf.^ or the tenth part of
the former.
This proves that on lines established on the system of
the Liyerpool and Manchester Railway, the chief profit is
to be expected from travellers; and it would be a self-
deception to reckon principally on the produce of the
goods. Such a result indeed was to be foreseen from the
consideration that, at the average price of places in the
coaches, 15 passengers pay to the Company, for the trip
between Liverpool and Manchester, the sum of 68
shillings, whereas the conveyance of a ton of goods is
paid only at the rate of 10 shillings and some pence for
the same distance.
From what has already been said of the maintenance of
the engines and of the road, on the Stockton and Dar-
lington Railway, it will readily be conceived that the total
expenses of haulage are much less on that line than on
the Liverpool and Manchester Railway. They are usually
quoted, approximatively, as amounting to one penny per
ton of coal carried 1 mile in the direction of the trade ;
but as the draught in the direction of the trade, on an
inclined line, does not give a precise idea of the effort
exerted, it will be proper here to make the calculation
in the same way as has been done for the Liverpool
and Manchester Railway.
The Company's accounts are divided imder three prin-
cipal heads, namely: locomotive power, maintenance of
way, and offices.
The first comprises charges of all kinds for repairs of
engines, engine-men's and assistants' wages, fuel, oil,
grease, hemp, and other articles of daily consumption for
conducting the engines and trains, llie second includes
workmen and materials for repairs to the road, new rails.
TOTAL BXPENSB OF HAULAGE. 565
draining, ballasting, repairs to bridges, walls, and fences,
and incidental expenses of the same nature. Lastly,
the office expenses include stationery and printing, clerks,
law disbursements, taxes, rates, police, and contingencies.
We have already seen that during the year from 3Gth
June, 1833, to 30th June, 1834, the expenses for loco-
motive power amounted to 'ISSd. per ton gross per mile
on a level (page 555); those for maintenance of way,
including the repairs to walls and fences, were '118rf.,
as was also proved above (page 557)* There remain then
only the office expenses, which, as will be seen, amount,
per gross ton per mile, to '037^.
Consequently, these three articles united give the total
expense of haulage per ton gross per mile, on a level, at
the velocity of 8 miles an hour, on the Stockton and
Darlington Railway, during that year :
Locomotive power •186''
Maintenance of road *118
Office 037
Total -341
As however the Company's expenses, that year, were
somewhat diminished by the circumstance that twelve of
the engines were then nearly new, we here subjoin the
same Company's expenses in the year following, in order
to compare them with those of the Manchester and Liver-
pool Railway.
From 30th June, 1834, to 30th June, 1835, these ex-
penses rose to the following rates :
Locomotive Power.
Expense per ton of goods or coals, drawn 1 mile in the
direction of the trade, from the Company's accounts,
-41830^; makes per ton gross per mile on a level,
(page 549) il^El •20915*'
566 APPENDIX.
MakUemmce of Road.
Expense per ton of goods or coals, drawn 1 mile, from
the Company's accounts, '20707'; makes, per ton
gross per mile, considering the weight of the wag-
gons and their return empty, (page 557),
•20707x|^ -10452
5*25
Office.
Expense per ton of goods or coals, drawn 1 mile, from
the Company's accounts, '07340^ ; makes per gross
ton per mile, according to the same proportion as
above -03705
Total per ton gross per mile on a level . . '35072^
And pel* effective ton per mile on a level, on a rail-
way without return of waggons empty (page 557),
•35072 X ^- -52277
2*65
These expenses do not include the repairs to the wag-
gons nor the expense for loading them, because the
waggons on this line belong to the coal-mine proprietors,
who bring them, moreover, to the railway all loaded and
ready to start. It will be proper then to add here the
former of those articles, on which the Company has con-
served some data.
When the Stockton and Darlington Railway Company
let out waggons, which it did till near the end of the year
1834, their repairs were found to amount to -^V Qf & penny,
or '0625e(. per ton of goods carried 1 mile, or, considering
the weight of the waggons and their return empty, to
2'65
•0625** X — — = •032*' per ton gross per mile. They cost
the coal-mine proprietors still less : some of these have
entered into a contract, on that account, at the rate of 1 5
shillings a year per waggon. Each waggon is reckoned to
TOTAL EXPENSE OF HAULAGE.
567
make^ on an average, two trips a week or 104 trips of 20
miles each in a year, with a load of 2*65 tons. This
bargain then makes the expense no more than *033rf. per
ton of coal, or 'Oljd. per ton gross per mile ; but we will
abide by the rate resulting from the Company^s books.
Moreover, we have seen that to render the expenses
of the Stockton and Darlington Railway comparable with
those of the Liverpool and Manchester Railway, an ad-
dition must be made to the former, representing the use of
coke instead of coal. And finally, among the Liverpool
expenses we are to take only those which occur on the
Darlington Railway; which will exclude the articles of
loading, cartage, and tunnel. With these alterations then,
and taking for the Darlington Railway, the expenses of
1834, the comparable expenses of the two railways are as
follow :
Total expense for haulage of goods on railways.
Designation of the articles of
expense.
Expenses per ton gross of
goods per mile, on a leveL
On the liver-
pool Railway,
at the velocity
of 12*5 miles
per hour.
On the Dar-
lington Rail-
way, at the ve*
locity of 8
miles per hour.
Locomotive power
Addition for coke instead of coal .
Maintenance of way
Repairs to waggons
Offices
•358''
•204
•115
•277
•209*'
•080
•105
•032
•037
Total ....
Loading, cartage, &c
Stationary engines and tunnels, &c.
Total ....
•954
•522
•034
•463
1^510
**
568 APPENDIX.
It has already been observed that on the Stockton and
Darlington Railway the waggons aire not kept with the
same degree of neatness as on the Liverpool and Man-
chester line. They are used only for the carriage of coal^
which admits of their being employed in any state. They
are constructed too with much less nicety^ their cost price
being but from £17 to £18^ instead of £30 or £36^
which those of Liverpool cost. Nor is the same expense
bestowed on the police of the road, and on divers acces-
sory objects. But as on a railway for slow motion^
destined to the conveyance of things of small value, less
care is necessary, it may be considered that, imder the
same circumstances, the same expenses are to be calcu-
lated upon.
Thus, recapitulating what precedes, with regard to the
total expenses of working railways at great velocity, with
simidtaneous conveyance of passengers and goods, and
railways at small velocity destined to the carriage merely
of materials of little value, it appears that on the former
the expenses of conveyance for passengers will be '721 d.
per passenger per mile on a level, and that the carriage of
goods, exclusive of loading, cartage, &c., may amount to
'95 d, or about 1 penny per ton gross per mile on a level;
but if the line is exclusively destined to the carriage of
goods, or rather to mine-work, it will be possible to
perform the conveyance of 1 ton 1 mile on a level, ex-
clusive of loading, cartage, &c., for *46d., or about ^ penny,
that is, for half the preceding sum.
Besides these expenses, which refer to the haulage
properly so called, the loading, cartage, &c., may occasion
an additional expense of '56 d* for every ton gross set in
motion, as is seen by the Liverpool and Manchester
Railway, which has furnished us with this amount.
».
OF HORSES AS A MOVING POWER. 569
Sect. VI. Of the expense of horses employed as a moving
power.
Having shown the difference of expense existing
between the two modes of conveyance mentioned above,
it will perhaps be well to say a word here upon the use of
horses. 'Hiis mode of conveyance being easy to establish,
may in certain circumstances be useful.
On the Stockton and Darlington Railway, where horses
were the moving power for many years, and were still so
in 1834, simultaneously with the locomotive engines, the
contract passed by the Company, for the hire of horses
with their drivers, on the principal line, was but for
i penny per ton of goods or coal conveyed 1 mile in the
direction of the traffic.
To know the price resulting from this, per ton gross on
a levely it must be remembered that one half of the
Stockton and Darlington Railway consists of descents
more inclined than the angle of friction, and that the other
half is sensibly level. It follows that through half the
way the horses have absolutely nothing to draw, and that
through the other half they have only to exert the regular
draught required by the same train on a leveL
Such is the work the horses have to perform in de-
scending the line with the loaded waggons. But moreover
and included in the same price, they have to convey back
the empty waggons up the line, that is to say, up an
average inclination of -^-fs-. This work, by reason of the
gravity on the plane, is nearly double that of drawing the
same empty waggons on a level.
Upon this line, then, the haulage of a waggon of goods
1 mile requires, in consideration of the inclination and
returns, the following traction :
2p
^70 APPENDIX.
1 loaded waggon, namely, 2*65 tons of goods descending
one mile, makes, including the waggon, 3*95 tons
gross carried ^ mile on a level, or 1*97/. carried 1 mile 1*97/.
The same waggon, weighing l'30^, brought back empty
up a plane inclined -j-^, equals, by reason of the
gravity, 3 tons conveyed the same distance on a level 3*00
Tons gross carried to 1 mile .... 4*97/.
Consequently the traction of 2*65 tons of goods one
mile descending^ produces a definitive traction^ to the
same distance on a levels of 4*97 tons, or 1*88 times as
much. The proportion is less here than in the case of
locomotive engines, because the weight is less by that of
the engines and their tenders.
Since the price paid for the hire of horses is '50 rf. for the
conveyance of 1 ton of goods 1 mile, it follows that the
locomotive power per ton gross per mile, on a level,
amounts to ='267^.
1-88
Consequently, adding the other articles above, we have
for the total expense of haulage relative to the use of
horses as a moving power ;
Hire of horses and drivers, or locomotive power . . . '267'
Maintenance of the road, as above '105
Offices, as above -037
Repairs to waggons, as above *032
Total per ton gross per mile on a level, exclusive of
loading, &c •441*'
3*95
And per eflectivc ton per mile on a level, '441** x — — •657*
^ 2-65
We perceive that these expenses are more considerable
than those of the Stockton and Darlington Railway
locomotive engines, with the use of coal, but nearly equal
to what would be necessary with the same engines, if coke
were used.
NET PROFITS. 571
Sect. VIL Of the net profits.
Before we pass on to the specified statements of the
receipts and expenses of all sorts of the Liverpool and
Manchester Railway Company^ we shall take down here,
from those same statements, the amount of the profits
made by the Company, from the opening of tiie railway.
This sketch will show that, if the mode of haulage in
question necessitates considerable expenses for its esta-
blishment, the profits it produces are fully adeqtiate to
indemnify speedily the Shareholders.
The road was opened to trade on September 16th,
1830, and from that period the dividends per share of
£100 sterling amounted to the following sums :
December 31, 1830 £2 0 0
Jane 30. 1831 4 10 0
December 31, 1831 4 17 8
Jmie 30, 1832 448
December 31, 1832 4 8 0
June 30, 1833 476
December 31, 1833 (besides a reserved
fund of £4,088 8«. lOcf.) 4 15 3
June 30, 1834 4 15 2
Total Sum from Sept. 16, 1830, to June 30,
1834, or in three years, nine months and
a half £33 18 3
This sum makes 9 per cent, per annum, notwithstanding
the reserved fund set apart by the Company, and the
extraordinary expenses inevitable at the outset of an
undertaking, which being the first of its kind, was neces-
sarily obliged to pay dearly for its own experience, whilst
future Railway Companies will have only to profit by the
experience acquired by their predecessors.
Besides this high interest for the capital invested, the
shares of this railway, from the original price of JCIOO
572 APPENDIX.
sterling, had risen^ after four years' establishment only^ to
£210; and have since been continually rising: and those
of the Stockton and Darlington Railroad bring in 8 per
cent, interest, and have risen in the short interval of
9 years from £100 to £300.
These plain facts make it unnecessary for us to add any
reflections.
We shall be happy if the elucidations already giv^en
with regard to expense, be of use to persons who may feel
inclined to engage in these speculations, which cannot SbuI
to be as advantageous to their private fortune as to the
prosperity of the country at large. But, to render this
part of our subject more complete, we shall conclude this
Appendix by giving the specified statements of the re-
ceipts and expenditure of the Liverpool and Manchester
Railway Company, from its origin, in September, 1830, till
the 30th June, 1834, at which period the Directors ceased
to render detailed accounts to the Shareholders.
EXTRACTS
PROM THE
REPORTS OF THE DIRECTORS OF THE LIVERPOOL
AND MANCHESTER RAILWAY.
PROM THE
Opening of the RaUway, on the 16M September, 1830, to the
ZOth June, 1834.
STATEMENT OF EXPENDITURE ON CAPITAL ACCOUNT.
Amount of expenditure on the construction of the way and the
works, from the commencement of the undertaking to 3l8t
December, 1833 £1,089,818 17 7
ANNUAL OR WORKING ACCOUNT.
PROM 16th SKPTSMBRR to 31st DICIMBIR, 1830.
Net profits of the Compi^ny £14,432 19 5
Dividend per share of £100 200
BALP-TBAR ENDING 30tH JUNB, 1831.
Net profits of the Company £30,314 9 10
Dividend per share of £100 4 10 0
HALF-TEAR ENDING 31 ST DECEMBER, 1831.
Tons.
Merchandise between Liverpool and Manchester . . . 52,224
Road traffic 2,347
Between Liverpool and the Bolton junction 10,917
Coal from Huyton, Eltonhead, and Haydock collieries,
brought by the Company's engines 7,198
Coal from Uulton brought by the Bolton engines . . . 1,198
574 APPENDIX.
Number of passengere booked at the Company's
offices 256,321
Number of trips of 30 miles performed by the
locomotive engines with passengers .... 2,944
Do. with goods 2,298
Do. with coals 150
Coach department £58,348 10 0
General merchandise 30,764 17 8
Coal department 695 14 4
£89,809 2 O
Expentet,
Office establishment £902 3 10
Coal disbursements 60 15 5
Petty ditto 110 0 5
Cart ditto 60 17 8
Maintenance of way 6,599 12 6
Charge for direction 297 19 0
Coach office establishment 589 5 9
Locomotiye power 12,203 5 6
Advertising 59 3 4
Interest 2,737 7 3
Rent 900 5 3
Compensation (coaching department) 156 7 5
Engineering department 625 0 0
Carrying dUbursements 10,450 12 3
Taxes and rates 2,763 5 I
Stationary engine disbursements 269 4 7
Coach disbursements 6,709 7 11
Waggon ditto 979 19 8
Compensation (carrying department) 786 8 2
Police establishment 1,490 14 1
Law disbursements 98 9 10
Bad debts 175 13 6
£49,025 18 5
Net profit from Ist July to 3l8t December, 1831 . . £40,783 3 7
Dividend per share of £100 4 10 0
Net profit on Sunday travelling per share of £100 . . 0 7 8
HALP-YKAK ENDING 30tH JUNK, 1832.
Tons.
Merchandise between Liverpool and Manchester . . . .54,174
Traffic to and from different parts of the road 3,707
Between Liverpool and the Bolton junction 14,720
Coals from different parts of the road brought by the
Company's engines 22,045
Coals brought by the Bolton engines 7,411
RECEIPTS AND EXPENDITURE.
575
Number of passengers booked at the Company's
offices 174,122
Number of trips of 30 miles performed by loco-
motive engines with passengers 2,636
Ditto with merchandise 2,248
Ditto with coals 234
Coaching department JC40,044 14
General merchandise department 32,477 14
Coal ditto 2,184 7
7
0
6
£74,706 16 1
Coach
disbursem^.
Carrying
disbursem^.
ExpeniBU,
Bad debt account
r- Guards' and porters' wages, ^
£1,104 4 6.~Parcel carts and
drivers' wages, £254 10 5.— -
Omnibuses and duty, £1,082 0 7.
— Repairs and materials, £1,777
9 4. — Gas, oil, tallow, &c., £228
14 6. — Stationery and sundry
disbursements, £441 1 7
Salaries, £1,749 5 lO.—PortersS
wages, £3,862 0 8.— Brakes-
men's wages, £461 5 9. — OU,
tallow, cordage, &c., £461 12 6.
—Carting, £808 16 5.— Repairs
to jiggers, trucks, &c., £163 14
11. — Stationery and sundry ex-
^ penses, £503 10 8
Coal ditto
Cartage (Manchester)
Charge for direction
Compensation (coaching)
Compensation (carrying)
Coach office establishment (Salaries, £573 13 1. —
Rent and taxes, £106 10 0.)
Engineering department
Interest
Fuel and watering, £2,957 8 0.
— Oil, tallow, hemp, &c., £507
3 1. — Repairs and materials,
£5,947 6 5. — Enginemen's wa-
ges, £1,170 18 8
Maintenance of way (wages, £3,929 8 0.— Blocks,
sleepers, chairs, &c., £2,668 12 3. — Ballast,
£733 0 3)
Office establishment (Salaries, £652 8 6.— Rent and
taxes, £77 9 2.— Stationery, &c., £81 10 5)
Police and gatekeepers
Petty disbursements
Rent
394 5 7
* 4,888 0 11
* 8,010 6 9
Locomotive
power.
26 8 10
1,420 4 9
308 14 0
101 10 9
288 10 3
680 3 1
520 9 0
5,966 14 11
10,582 16 2
7,331 0 6
811 8 1
1,356 9 11
75 1 0
1,840 1 10
576
APPENDIX.
Stationary engine and tunnel disbiinements, new
tunnel rope, £330 10 S.^Coal, Je265 7 0.—
Wages, £290 9 9.— Bepairs, ml, tallow, hemp,
&c., £165 8 9 £1,051 16 2
Taxes and rates 1,109 14 9
Smiths' and joiners' wages, £586 ^
6 7. — Iron, timber, &c., £265
0 9. — CauTass, paint, &c., for
sheets, £155 10 10
Waggon
disbursem**.
*• 1,006 18 2
47,770 15 5
Deduct credits 1,112 4 1
<£46,(»S8 11 4
Net profits tor six months :£28,048 4 9
Dividend per share of £100 400
Net profit on Sunday traTelling per share of £100 . . 0 4 8
HALT-TEAR ENDING 31ST OKCEMBER, 1832.
Tons.
Merchandise between Liyerpool and Manchester .... 61,995
Ditto to diiTerent parts of the road, including the
' Warrington and Wigan trade, .... 6,01 1
Ditto between Liverpool and Bolton 18,836
Coals from various parts of the road to Liverpool or Man-
chester 39,940
Number of passengers booked in the Company's
ofllces 182,823
Number of trips of 30 miles performed by the lo-
comotive engines with passengers .... 3,363
Do. with goods 1,679
Do. with coals 211
Receipts.
Coaching department £43,120 6 11
General merchandise 34,977 12 7
Coal department 2,804 3 4
Expeiuee,
Bad debt account
^Guards' and porters' wages, -^
£1,173 19 6. — Parcel carts
and drivers' wages, £375 14 4.
— M'aterials for repairs, £464
1 9. — Men's wages, repairing,
£613 18 1.— Gas, ofl. taUow, ^
&c., £232 11 7.— Duty on pas-
sengers, £985 19 L— Station-
cry and petty expenses, £414
'^ 19 7
Coach
disbursem^. *
£80,902 2 10
£81 6 0
4,261 3 11
RECEIPTS AND EXPENDITURE.
577
Carrying
fUsbusem**.
Locomotive
power.
SaUries, £1,822 13 2.->Por.
ter»', &c., wages, £3,925 7 4.—
Gas, oil, tallow, cordage, &c.,
£296 11 r.—Repairs to jig-
gers, tracks, stations, &c., £398
3 11. — Stationery and petty ex-
penses, £540 13 5 ....
Coal ditto
Cartage (Manchester) '
Charge for direction
Compensation (coaching)
Ditto (carrying)
Coach office establishment (Salaries, £556 3 10.—
Rent and taxes, £75 15 2)
Engineering department
Interest
" Fuel and watering, £3,848 10 8.
—Oil, tallow, hemp, &c., £661
1 9. — Materials for repairs,
£3,723 9 7.— Men's wages, re-
pairing, £3,352 16 2.— Engine
and firemen's wages, £1,060
in 6
Law disbursements
Maintenance of way (wages, £3,675 16 5. — Blocks,
sleepers, chairs, dec, £2,355 17 1. — BaUast, &c.,
£846 10 9)
Petty disbursements
Rent
Stationary engine and tunnel disbursements, (Coal,
£209 15 3. — Engine and brakesmen's wages,
£316 7 5.— Repairs, gas, oO, tallow, &c., £326
14 7)
Taxes and rates
Smiths' and joiners' wages, £583 "
0 5. — Iron, timber, &c., £350
12 10. — Canvass, paint, &c., for
sheets, £31 0 0
Office establishment (Salaries, £623 18 0. — Rent,
£85 0 0.— Stationery, £18 9 0)
Police ditto
Waggon
cUsbursem^.
> 6,983 9 5
27 2 10
2,744 18 7
295 1 0
209 15 11
150 19 11
631 19 0
450 0 0
4,555 15 7
12,64« 9 8
118 3 8
6,878 4 3
66 2 0
1,246 5 0
852 17 3
3,483 18 2
964 13 3
727 7 0
902 16 5
Net profit for six months
Dividend per share of £100
Net profit on Sunday travelling per share of £100
£48,278 8 10
£32,623 14 0
4 4 0
0 4 0
BALr-YBAR ENDING 30tH JUNK, 1833.
Tons.
Merchandise between Liverpool and Manchester .... 68,284
Ditto to different parts of the line, including War-
rington and Wigan 8,712
Ditto between Liverpool, Manchester, and Bolton . 19,461
Coals from various parts, to Liverpool and Manchester . . 41,375
578
APPENDIX.
Total number of passengers booked in the Co/s
offices 171,421
Number of trips of 30 miles performed by the
locomotive engines with passengers .... 3,262
Ditto with merchandise 2,244
Receipts.
Coaching department .£44,130 17 2
Merchandise ditto 39,301 17 3
Coal ditto 2,638 15 9
X86,07I 10 2
Eapensef,
Coach
disbursem'*.
Advertising account
Bad debt account .........
^Guards' and porters' wages, -^^
£1,150 4 0. — Parcel carts,
horse keep, and drivers' wages,
£401 18 6.— Materials for re-
pairs, £383 15 11. — Men's
wages, repairing, £758 10 6.
— Gas, oil, tallow, cordage, &c.,
£324 4 0. — Duty on passengers,
£2,466 15 4. — Stationery and
petty expenses, £236 15 6. —
Taxes on offices, stations, &c.,
^£112 18 4
"Agents' and clerks' salaries,"
£1,703 17 6. — Porters' and
brakesmen's wages, horse keep,
&c., £4,687 9 7.— Gas, oil,
tallow, cordage, &c., £648 4
» 11. — Repairs to jiggers, trucks,
stations, &c., £405 13 l.->
Stationery and petty expenses,
£336 9 0. — ^Taxes, insurance,
&c., on offices and stations,
L£798 18
Coal disbursements
Cartage (Manchester)
Charge for direction
Compensation ^coaching)
Compensation (carrying)
Coach office establishment (Agents' and clerks' sa-
laries, £577 19 6.— Rent and taxes, £102 17 1)
Engineering department
Interest
£50 8 7
176 18 6
> 5,835 2 1
Carrying
disbursem^.
» 8,579 15 9
120 16
2,460 16
252 0
38 1
1,033 18
1
1
0
2
3
680 6
441 17
5,367 11
7
4
9
RECEIPTS AND EXPENDITURE.
579
Locomotive
power.
> 14,715 16 9
Coke and carting, £2,795 4 5.
— Wages to coke fillers, and
watering engines, JS338 16 10.
— Gas, oil, tallow, hemp, &c.,
J6760 15 2. — Copper and brass
tubes, iron, timber, &c., for
repairs, £3,290 8 8. — Men's
wages, repairing, £4,115 0 8.
Enginemen and firemen's wages,
£892 4 4.— Outdoor repairs to
engines, £943 6 8. — ^Two new
engines, " Leeds" and " Firefly,"
£1,580 0 0
Maintenance of way (wages, £3,648 18 5. — Blocks,
sleepers, cheiis, &c., £2,052 5 11. — Ballast and
draining, £1,013 4 11) 6,714
Ofiice establishment (Salaries, £624 19 0.— Rent
and taxes, £62 18 6.— Stationery, &c., £56
19 5)
Police
Petty disbursements
Rent
Repairs to vralls and fences
Stationary engine and tunnel disbursements (Coal,
£155 8 1. — Engine and brakesmen's wages, £363
8 10.— Repairs, gas, oU, Ullow, &c., £340 15 11)
Tax and rate 1,891
Waggon disbursements (Smiths' and joiners' wages,
£598 3 1.— Iron, timber, &c., £320 1 4.— Cord-
age, paint, &c., for sheets, £82 7 3) ....
Cartage (Liverpool)
744
950
70
601
296
859
9 3
16
4
0
15
4
12
0
1,000 11
18 4
11
7
0
8
2
10
7
8
6
£52,900 9 1
Net profit for six months
Dividend per share of £100
Net profit on Sunday travelling per share of £100
£33,171 1 1
4 4 0
0 3 6
HALV-YKAR ENDING 31ST DECEMBER, 1833.
Tons.
Merchandise between Liverpool and Manchester .... 69,806
Ditto to and from different parts of the line, includ-
ing Warrington and Wigan 9,733
Ditto between Liverpool, Manchester, and Bolton . 18,708
Coal from various parts to Liverpool and Manchester . . 40,134
Total number of passengers booked at the Co«'s
ofiSces 215,071
Number of trips of 30 miles performed by the
locomotive engines with passengers .... 3,253
Do. with merchandise 2,587
580
APPENDIX.
Heceipts.
Coaching department £54,685 6 11
Merchandise ditto 39,957 16 8
Coal ditto 2^91 6 6
Je9 7,234 10 1
Expenset,
Advertising account
Bad debt account
6 10
374 10
Coach
disbursem^. '
Carrying
disbursem^.
"Guards' and porters' wages,
£1,168 4 6. — Parcel carts, horse
keep, and drivers' wages, JS361
I 7. — Materials for repairs,
£689 12 6.— Men's wages, re-
pairing, £1,041 1 3.— Gas, oil,
tallow, cordage, &c., £196 4 11.
— Duty on passengers, £3,224
II 11. — Stationery and petty
expenses, £277 4 5. — Taxes
on offices, stations, &c., £116
0 8. — Guards' clothes, £64
15 0.*
"Agents' and clerks' salaries,
£1,728 16 9. — Porters' and
brakesmen's wages, horse keep,
&c., £5,006 6 10.-— Gas, oil, tal-
low, cordage, &c., £529 17 0. —
Repairs to jiggers, trucks, sta-
tions, &c., £366 9 11.— Sta-
tionery and petty expenses, £429
5 1. — ^Taxes and insurance on
offices, &c., £456 17 7.— Sacks
(^forgndn, £110 3 10 ....
Coal disbursements
Cartage (Manchester)
Charge for direction
Compensation (coaching)
Compensation (carrying)
Coach office establishment (Agents' and clerks' sa-
laries, £602 6 8.— Rent, £30)
Engineering department
Interest
f Coke and carting, £3,197 4 4.
— ^Wages to coke fillers and
waterers, £348 8 5. — Gas, oil,
tallow, hemp, cordage, &c.,
£865 14 9. — Brass and copper,
iron, timber, &c., for repairs,
£3,755 3 7.— Men's wages, re-
pairing, £4,401 4 10.— Engine
and firemen's wages, £784 8 5.
— Out-door repairs to engines,
£613 3 9
Locomotive
power.
0
1
* 7,138 16 9
' 8,627 17 0
82 0 9
3,173 18 0
312 18 0
142 4 8
223 10 11
632 6 8
319 3 4
5,140 6 4
> 13,965 8 1
1
RECEIPTS AND EXPENDITURE.
581
Mainte-
nance of
way.
^ 6,425 14 8
^ Wages to plate-layers, joiners,^
&c., £2,937 19 2. ~ Stone,
blocks, sleepers, keys, chairs,
&c., £2,411 2 4.-> Ballasting
and draining, £925 16 11. —
^ New rails, £150 16 3 . . . .
Office establishment (Salaries, £607 2 0.— Rent
and taxes, £75 14 3. — Stationery and printing,
£22 7 8.->Stamps, £17 2 3)
Police
Petty disbursements
Rent
Repairs to walls and fences
Stationary engine and tunnel disbursements, (Coal,
£302 6 5. — Engine and brakesmen's wages,
£319 11 2. — Repairs, gas, oil, tallow, &c.,
£419 15 5.— New rope for tunnel, £266 3 6) .
Tax and rate
" Smiths' and joiners' wages, £718
19 7. — Iron, timber, castings, &c.,
£700 9 1.— Cordage, paint, &c., y I fill 0 3
£28 5 2.~Canyas8 for sheeta,
L £163 6 5
Cartage (Liverpool)
Law ^bursements
722 6 2
1,022 7 6
61 19 6
603 10 8
665 3 4
1,307 16 6
3,409 11 0
Waggon
disbursem**.
80 17 10
300 3 9
Net profit for six months
Dividend per share of £100
Net profit on Sunday travelling per share of £100
Reserved fond formed in the six months . . .
£56,350 1 9
£40,884 8 4
4 10 0
0 5 3
4,088 8 10
HALF-YBAR ENDING 30tH JCNX, 1834.
Tons.
Merchandise between Liverpool and Manchester .... 69,522
To and firom different parts of the road, including Warring-
ton and Wigan 15,201
Between Liverpool, Manchester, and Bolton 19,633
Coal to Liverpool and Manchester 46,039
Number of passengers booked at the Company's
offices 200,676
Number of trips of 30 miles performed by the
locomotive engines with passengers .... 3,317
Ditto with merchandise 2,499
Coaching department £50,770 16 11
Merchandise ditto 41,087 19 5
Coal ditto 2,925 15 11
Experuei.
Advertising account £16 15 0
Bad debt cUtto 75 12 3
£94,784 12 3
582
APPENDIX.
Coach
disbarsem^.
Carrying
disbursem**.
Guards' and portera' wagea»<^
£1,167 11 10.— PaitMd carta,
horse keep, and drivers' wages,
£359 13 0.— Materials for re-
pairs, £1,007 9 7. — Men's wages,
repairing, £1,221 15 5.— Gas,
oil, tallow, cordage, &c., £358
15 6. — Duty on passengers,
£3,008 1 11.— Stationery and
petty expenses, £165 2 5. —
Taxes, insurance, &c., on offices
and stations, £65 8 11 ...
^Agents' and clerks' salaries,''
£1,740 14 2. — Porters' and
brakesmen's wages, horse keep,
&c., £5,397 8 5. — Gas, oil,
tallow, cordage, &c., £708 17 4.
— Repairs to jiggers, trucks, sta-
tions, &c., £716 2 8. — Sta-
tionery and petty expenses,
£290 3 2.— Taxes, insurance,
&c., on offices and stations,
£469 6 2 ^
Coal disbursements
Cartage (Manchester)
Charge for direction
Compensation ^coaching)
Compensation (carrying)
Coach office establishment (Agents' and clerks' sa*
Uiries, £615 1 11.— Rent and taxes, £63 1 1) .
Engineering department
Interest
" Coke and carting, £2,882 11 4.
— Wages to coke fillers, and
watering engines, £386 19 5. —
Gas, oil, tallow, hemp, &c., £881
18 4. — Copper and brass tubes,
iron, timber, &c., for repairs,
£4,140 19 6.— Men's wages for
repaiiing, £5,432 8 8. — ^Engine-
men and firemen's wages, £836
14 3. — A new engine, £700. —
Lathe engine, boiler and fixing
for repairing sheds and watering
t. stations, £380 6 4 ^
Law disbursements
^ Wages and small materials,.^
Twioi-«#* £4,221 2 5.— Stone, blocks,
n2n^ of J "^««P«"' ^'* ^^'^®2 18 7—
nance or < ^^^ ^^^ ^^ ^^. __._._
7,353 18 7
9,322 11 11
45 1 0
2,988 6 2
289 16 0
26 3 10
645 6 0
678 3 0
352 10 0
5,546 4 0
Locomotive
power.
* 15,641 17 10
way.
i, points, r
14 5.—
t93 2 0 .^
100 0 0
9,350 17 5
crossings, &c., £3,153
^ Ballast and leading, £493
Office establishment (Salaries, £818 14 4.— Rent
and taxes, £58 8 0)
Police
Petty disbursements
Rent
877 2 4
1,016 18 1
60 0 0
363 11 11
RECEIPTS AND EXPENDITURE.
583
Stationary engine and tunnel disbursements, (Coal,
;6327 12 1. — Engine and brakesmen's wages,
£3Sb 7 0.— Repairs, gas, oU, tallow, &c., £273
111)
Tax and rate
^Smiths' and joiners* wages,
£773 3 8.— Iron, timber, &c.,
£728 12 4.— Cordage, paint,
&c., £109 19 2.— Canvass for
[^ sheets, £240
Repairs to walls and fences
Cartage (LiYerpool)
Waggon
disbursem**. **
986 10 2
1,778 16 10
1,851 15 2
644 0 11
80 17 6
Net profit for six months
Dividend per share of £100
Net profit on Sunday travelling per share of £100
£60,092 15 11
£34,691 16 4
4 10 0
0 5 2
THE END.
PRINTED BY W. HUOHB8,
king's head court, OOUOH SQOARK.
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WORKS RECENTLY PUBLISHED
ON THE VARIOUS BRANCHES OF
ARCHITECTURE, CIVIL AND MILITARY ENGINEERING,
MECHANICS, NAVAL ARCHITECTURE, &c. &c.
BY JOHN WEALE,
ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN,
^here on Eaptefuive Stock of all the approved PubUcattom relatinff to the above Subjects^ and the
Fine Arts, whether Foreign or Domeetic, is constantly on Sale.
1.
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I STUDIES OF MODERN ENGLISH ARCHITECTURE.
THE TRAVELLERS' CLUB-HOUSE.
By CHARLES BARRY, Architect.
Illustrated by Engrayings of Plans, Sections, Elevations, and Details, by J. H. Le Ks0x.
With an Essay, including a Description of the Building, by Mr. W. H. LEEDS.
\* This volume, complete in itself, is proposed as the first of a series under the general title of ** The
Modem School of English Architecture.''
' The Plates, engraTed by J. H. Le Keux, from the Drawings of Mr. Hewitt, are examples of
perfection in this species of art. We do not believe that any artists that ever Uved could carry it
further. They will afford exemplars both to architectural draughtsmen and engravers, as well as to
architects themselves; and will go down to posterity as the remains of Grecian architecture have
descended to us.
' The author before us seems to be exactly the sort of commentator to grapple with doubts and'
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bines fresh thoughts and sound reflections on his subject with good taste and elegant diction.' —
Probe, No. 13. i
2.
50 Plates, neatly engraved. Imperial 4to., Price £2, 8s.
ORNAMENTAL IRON WORK.
0ATE8, LODGES, PALISADING, AND RAILS OF THK ROTAL PARKS;
With some others, including the Entrances to the Sultan's Palace at Constantinople.
Part. I. is just published, containing 25 Plates, Price £1. 4s. Part. II. vrill be published in Feb., 1840.
The work consists of Engravings of Plans of Regent's, Hyde, and St. James's Parks, the Lodges,
Entrance Gates, Ornamental Rails, &c. ; with those of Hampton Court and Greenwich; the Gates
manufactured in this country for the Sultan's Palace, together vrith other very interesting examples of
the modem improved style. Designed principally by John Nash, Decimus Burton, &c., Architects ;
with some of the old style by Inigo Jones, Sir Christopher Wren, &c.
<
WORKS PUBLI8HBD BY JOHN WBALE,
3.
TREDGOLD ON THE STEAM ENGINE
AND
ON STEAM NAVIGATION.
These very important and interesting volumes, comprising 125 very elaborate and beautifully engraved
Plates, are, in Sections, Elevations, Plans, Details, &c., of the highest utility to the Engineer and
Student, to Manu^turers of Marine, Locomotive, and Land Engines ; — ^the science being elnddated
and explained by the most eminent practical men of Britain. In 2 4to. vols., price £4. 4#., entitled
THE STEAM ENGINE;
Comprising an account of its invention and progressive improvement, vrith an iNTSsnoAnow of iu
PRINCIPLKS, and the proportions of its parts for kppicibnct and streno'th ; detailing also it^
application to Navigation, Mining, Impelling Machines, &c., and the Result in mtmeioiu Tables
for Practical Use, with Notes, Corrections, and New Examples, relating to Locomotive and other Engines.
Rbvisbii and Edited by W. S. B. WOOLHOUSE, F.R.A.S., &c
The algebraic parts transformed into easy practical Rules, accompanied by Examples familiiri)
explained for the Working Engineer, with an ample
APPENDIX,
Containing, besides a vast acquisition of Practical Pinters, an Elementary and Practical Description of
Locomotive Engines now in use, illustrated by Examples ; and the Principles and Practicse of Steaii,
for the purposes of Navigation either in Rivers or at Sea ; showing its present and progressive state, by
illustration of the various Examples of Engines constructed for Sea, War, and Packet Vessels, and River
Boats, by the most eminent MaJcers of England and Scotland, drawn out in Plans, Elevations, ScetkmSf
and Details, with a Scientific Account of each, and on
STEAM NAVAL ARCHITECTURE,
Showing, by existing and the latest Examples, the Construction of War, Sea, and Packet VesMls : their
Naval Architecture, as applied to the Impelling Power of Steam for Sea and River purposes. This
portion of the work is edited by several very eminent Ship Builders —
OLIVER LANG, Esq., of H.M. Dock-yard, Woolwich,
J. FINCHAM, Esq., H.M. Dock-yard, Chatham.
T. J. DITCHBURN, Esq., Depfifozd and BlackwaU.
The new subjects in this edition consist of the works of
Messrs. Boidton and Watt William Morgan, Esq.
The Butterley Company. Messrs. Hall, Dartford.
Messrs. MaudsUy, Sons, and Field. Edward Bury, Esq., liverpooL
Messrs. Seaward. Messrs. Hague.
Robert Napier, Esq., Glasgow. Messrs. Claude, Girdwoord, and Co.
Messrs. Fairbaim and Murray. Messrs. R.Stephen8on and Co.,Newc8Stlettp<mTyne.
Bttsiaiitts^ &9 ^tvmMian^ to fger ^iUieirts.
LIST OF PLATK8.
1. iMnneCriealpnycetlaiiof ftfceteBgularttesmboilar.
2. Two MetioiM of a cylindrical steam boiler.
3. Brunton'a apparatoa for feeding furnaces by machinery.
4. High prenure engine with four-paMaged cock.
6. Section of a doable acting condensing engine for work-
ing ezpansiTely.
0. Section of a common aimoapheric engine.
7. Represents the construction of pistons.
8. Parts of Fenton and Murray's double engine.
9. Apparatus for opening and closing steam passages.
10. (A). 10 (B). Parallel motiooa or eombinatums oaed to
produce rectilinear motion from motion in a circular arc.
11. Plan and elevation of an atmospheric pompiag engine
for rainng water fkom a mine.
IS. Boolton and Watt's single acting engine.
IS. Double acting engine for raisins water.
14. ^for impelling machinery, by Fen-
>
ton, Murray ft Co.
15. Maudslay's portable engine.
lO. Indicator for measuring the foree of steam in the
cvlinder.
-^Diagrami to iUnstrafee Che comparathre stability of
opposite diiifs of vessels.
17. Sectitm of a steam vessd with its boiler in two parts.
18. Isometrical projection of a steam boat engine as first
arranged br Boulton and Watt.
19. Section and plan of steam boat engine.
M. Side elevadon and
91. Kingston's valves.
blow-off valves.
iiyection valres.
hand pump valves.
as. Boilers of Her Muesty's steam vessel
53. Boilers of Her Mucsty's steam frigate Medea.
54. Paddle wheels of Momn and Seaward.
55. Positions of a float 01 a radiating whed. and also of a
vertical acting wheel, in a vessel m motioo.
96. Qydoidal paddle wheel fitted to the Great Western.
27, 98. Illustrate Captain Oliver's paper.
99. ExhibUs the various situations cSf a trial at sailing ftf
the Medea, with the Caledonia, Vancnaid, and Asia.
SO. Side view oS the engines of the Red Bover, and Citr^
Canteibury, steam vessels*
31. Longitudinal section of ditto.
39. Cross section of engines of ditto.
8S. Side devaCion of the enf^ of the NBe ateam sh^^.
84. Plan of the engine of the Nile.
35. SO. Cross sections of engines of the NQe.
37, S8, 89. Enoines of Her Mi^esty's sleam ft%al» Aomb.
40. Engines of the Ruby Gravesend padbst.
41. Seraon oS one of the engines of the Dosi Joan Ptain>
sula Company*s packet.
43. BoUers of Her Mi^ty's ships Hcnnca, Sjpstfife, and
Firefly.
4
iLt.
ARCHITECTURAL. LIBRARY, 59, HIGH HOLBORN.
3
®
■g;v
j^
i.
44, 45, 46. Elevation, plan, and two aectioa* of the
enginea of the armed Ruaaian steam ships Jaaon and
Colchis.
48. Hall'a improvementa on steam enginea.
50. Enginea m Her M^jeatj's steam ship If enenu
68, 53, 54. Engines of the Hull and London packet
William WUbexforee.
(A). Longitudinal aeetion of Humphiys's patent marine
engine.
(B). Longitudinal eleration of Humphrya's marine
engine.
(A). Midahip section of the steam packet Dartford,
ahowing a nont deration <rf a pair of Humphrys's
engines.
(B). Flan of the engines of the Dartford.
58, 50. Forty-five horse power engine, constructed by
W. Fairbaim and Co.
61, 03, 63. Ten-hone power engine, eonatmeted by
W. Fairbaim & Co.
Elevation of a locomotive engine, Stanhope and Tyne
Riulway; constructed by Messrs. B. Stq»henaon and
Co., of^Newcastle upon Tym*
Secdon of ditto.
Safety valvea of ditto.
(A). Cylinder oorwr and eonneetiBg rods of ditto^
(B). Cylinder and piston at large or ditto.
Plan and section of boiler seating for a twenty-horse
engine, at the manufactory of Messrs. Wbitworth and
Co., Mancheater.
Messrs. Hague'a double acting cylinder, with slides, &c.
'.,, * The flnt publication of Mr. Tredgold's work,
r^n one of the most important mechanical and
" cientific subjects of oiir age, was so highly suc-
ressfiil, that, besides being translated into the
Prench, and, we belieTe, other languages, a new
ifsdition was imperatively called for. That call
?ha8 been answered by the present enlarged work,
in which has been embodied the progress and
improved application of that mighty agent Steam,
an investigation of its principles, and a practical
view of its uses and effects in steam vessels, steam
carriages, and railroads. When we look around
us and see the face of the country changed and
changing; the expedition of a week compressed
into a single day; the limits of pleasure and of
business widely extended among all classes of
society; new wants created, and new wishes
gratified; sedentary easily and readily converted
' into ambulatory life ; the sphere of ci^ homes, as
it were, enlarged by a circle of rural miles;'-
when, in fsct, we see the prodigious alteration
made in our social, statistical, economical, po-
litical, national, and international system, by the
growing powers of this vast engine, we cannot
but consider the effort to offer us a just and com-
prehensive account of it to be one of the most me-
ritorious within the scope of individual industry,
skill, and labour. We, therefore, think the public
deeply obliged to Mr. Tredgold, the author, and
Mr. Weale, the enterprising publisher, who must
have expended a very large sum on the risk, for
the very important volumes now before us.
* It is apparent that it is a publication of great
magnitude and great worth. Above a hundred
plates of steam engines, &c. &c., illustrate its
descriptions; and many wood-cuts serve further
to render the contents plain and intelligible to
every capacity. Thus the actual operations of
such men as fioulton and Watt, Maudslay and
Field, Seavrards, Napier of Glasgow, and other
eminent mechanicians, and, we may add, en-
^
70, (A). 70 (B). Sections of the engines of the Berenice
steam vessel.
71, 7S. Beale's patent rotatory engine.
73. Mr. Ayre's contrivance for preventing a locomotive
engine from running off a railway.
74 to 83. Belate to the very important subject of aU kinds
of paddle wheels.
84 to 88. Sixty-five inch cylinder engine, erected by
Messrs. Maudslay, Sons, and Field, at Chelsea water-
works.
89 to 02. Patent locomotive engine, made by Meaars. R.
Stephenson and Co. for the London and Birmingham
Railway.
98. Drawings of the Comet, the first steam boat in Europe.
94. The Pacha's steam vessel of war, the Nile.
95, 90. The Hon. Eaat India Company's steam vessel
Beremce. «
97. Draught of the Forbes steamer, Chineae rigged.
98. Heme Bay steam packet Red Rover.
99. Diamond Company's steam packet Baby.
100 to 103. Her M igeaty's steam veasel of war Medea.
104 to 107. Conatruetion of the Nile ateam ship, built for
the Pacha of Egypt.
108, 109, 1 10. His Imperial Majesty's armed ateam veaael
Colchis.
Ill, 111 (A). Enffinea of the steam ship Tiger.
1 la. The Admiralty yacht Firebrand.
113. Portrait of the late Mr. Watt.
1 14. Portrait of the late Mr. Tredgold.
115. 117, 118. Illustrate steam navigation in America.
lightened philosophers as well as experienced
artisans, are explained to us, and set before our
eyes so as to be palpable to the understanding.
In the same way the locomotives of the Messrs.
Stephenson, of Newcastle, the construction of
the elegant government steam boats of Mr. Lang,
of Woolwich, and Mr. Fincham, of Chatham, (ves-
sels it is a delight to notice as we pass up or
down the river,) are rendered familiar to us ; and
we care little to vex ourselves about hypothetical
improvements and untried experiments. We have
witnessed so many pseudo certain and undeniable
inventions fail, that we have become rather scep-
tical when we hear of patents that are to supersede
all that has been done before, or listen to the dic-
tatorial laws of people whom we have known to
be more frequently wrong than right. We are
glad to observe, however, that in this new edition
most of the errors of the former have been cor-
rected; and what questionable statements or
mistakes may remain are not such as to impeach
the vast utility of the publication.
' The Appendix, indeed, is deserving of much
praise. The rules of practice are well expounded,
and the mathematical calculations, remodified into
simple arithmetic, are excellent for the purpose of
enabling the working man ("operative'' is the
fsshionable phrase) to perform. his duty.
' Upon the whole, not to dwell upon either real
or supposed imperfections, inseparable from a
production embracing so vsst a number of com-
plicated matters — a production treating of things
in an almost daily state of partial transition — ^we
feel bound to pronounce this treatise to be a very
able and satisfactory exposition of the state of
steam navigation and railroad travelling to the
present time ; and as such we heartily recommend
it to the public at large, both at home and on the
continent, where its predecessor has hitherto been
esteemed a standard work.' — Literary Gazette,
Auguet 3, I839.
4
WORKS PUBLISHED BY JOHN WBALE,
4.
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TREDGOLD ON THE STEAM ENGINE AND ON STEAM NAVIGATION
5.
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TREDGOLD ON THE STEAM ENGINE AND ON STEAM NA\aGATIO>
\* This work having been selected as a Prize-book by the Institution of Civil Engineers, isd # -
other Institutions, and by practical Engineers for presents to their Pupils, can be had in any <ftb£* '
of binding by giving seven days' notice.
6.
In 2 vols., very neatly half-bonnd in red morocco, gilt tops ; the Text in quarto, and the Plate? prc
separately on tine Columbier folio paper, Price £7. 7«.
TREDGOLD ON THE STEAM ENGINE AND ON STEAM NAVIGATION
7.
The Plates sold separately, on Columbier folio, very neatly half-bound in red morocco, gilt tops
Price £5. 5«.
TREDGOLD ON THE STEAM ENGINE AND ON STEAM NAVIGATIO
\* In many instances purchasers of the work in 2 vols, have also possessed themselves ol '.i*
Plates in a separate form, not only for practical use and reference, but as a Table-book, to exhi^ •
splendour of the Steam Machinery of Britain.
8.
In quarto size, with four elaborately engraved Plates, and numerous Wood-cuts of Detafla, Priee £!■ '
in cloth boards.
DESCRIPTION OF the PATENT LOCOMOTIVE STEAM ENGLV:
OF Messrs. ROBERT STEPHENSON and Co.,
NBWCASTLS UPON TTNS.
*4i* The above Work is affixed to the publication of the 2nd edition of Tredgold, and has been ps^
lished separately for the use of those who desire a perfect knowledge of the Locomotive Eeprl
separate from other Steam Engines. The description is both popular and scientific, and was draws . I
under the immediate superintendence of Robert Stephenson, Esq. The Engravings aire large,, and iM
unique examples of mechanical engraving. The cost of the four Plates was £400 ; the «ood-<c*j
40 in number, are explanatory of such details of the Engine as cannot be shown in the £levatir-|
Plan, Cross or Transverse Section ; nor so well described in language as by the ocular demcNistntioB -fl
these, intermixed as they are with the descriptive text. It will be found that this extraordinaiy mooe'i
Engine, which owes its present improvements to the Stepbensons, is made available to tht i&illk»:
being explained in the plainest language, and divested of mathematical foimulas,
9.
STEAM NAVIGATION.
Just published, in Atlas folio size, uniform with Telford's works and the Atlas copies to Tred*oid.
Price 12*. ®
APPENDIX A, TO THE NEW EDITION of TREDGOLD ox ri::
STEAM ENGINE.
CONTENTS.
Plate I. — Iron Steam Yacht G^/ow^tPorm.constructed power each, 50>inch cylinders, 4-6 itiolce. m^
by John Laird, Esq., Birkenhead, Liverpool. by G. Forrester and Co., of Livetpod, and fin->
Plates II. and III. — Iron Steam Ship Hambowt on board of the Rainbow,
belonging to the General Steam Navigation Plate V. — Side Elevation and Sectioii of ditta
Ck>mpany, draught lines at bottom, fore body Plate VI. — ^Transverse Section of ditto,
to a Urge scale, by Ditto. Plate VII. — Draught of the Americui Anr-
Plate IV. — Plans of the Engines of QO-horse Steam Ship Fulion, Half the main brtra?:!
W^'
ARCHITECTURAL LIBRARY^ 59, HIQH HOLBORN.
17 feet: distance between the water lines, 2
feet ; fore and after body precisely alike.
Plate VIII. — Plana of the Upper and Lower
Decks of the Admiralty Yacht Firebrand^
showing the fittings and conveniences; drawn
Plates IX. and X. — Plans of the Upper and Lower
Decks of the Iron Steam Ship Nevkot con-
structed for Her Imperial Majesty the Empress
of Russia, by Messrs. Fairbaim and Murray, of
Mill MTall, Poplar.
by Mr. James Henry Lang, of Woolwich.
APPENDIX B. is in preparation. To contain the remaining five Engravings of the Nevka, the
Steam Engine in the Royal Arsenal at Woolwich, and other interesting subjects ; together with the Text
for both Parts. Price 12«.
10.
Just published, vol. 3, with several Plates, Price £1, hi.
PAPERS ON SUBJECTS CONNECTED WITH THE DUTIES OF
THE CORPS OF ROYAL ENGINEERS.
CONTENTS.
Introclucilon.
Memoranda relative to the Lines thrown up to
cover Lisbon in 1810. By Colonel John T.
JoNBS, Royal Engineers.
Memoranda relating to the Defence of Cadiz, and
explanatory details of the Position intrenched
by the British troops under Lieutenant-General
Graham, in 1810.
Instructions of the Minister of War concerning
the Model-towers approved of by Napoleon.
Translated by Lieut. Laffan, Royal Engi-
neers.
Report on the Demolition of the Revetments of
some of the Old Works at Sheemess, on Sa-
turday the 14th July, 1827.
Letter from Lieut.-Colonel Robert Thomson to
Lieutenant Denison on the subject of Furnaces
for heating Shot.
Memoir on Posen, by T. R. Stavelt, Esq., late
Captain Royal Engineers.
Report on Beaufort Bridge. By R. J. Nelson,
Lieutenant Royal Engineers.
Rough Sketch of the Suspension Bridge over the
Lalm at Nassau. By R. J. Nelson, Lieutenant
Royal Engineers.
Detailed Description of some of the Works on th^
Rideau Canal, and of the alterations and im-
provements made therein since the opening of
the navigation. By Lieutenant Denison, Royal
Engineers.
On the mode of Bending Timber adopted in
Prussia. By R. J. Nelson, Lieutenant Royal
Engineers.
Description of the Coffer-dam used in the Con-
struction of the Piers of the Alexandria Aque-
duct, being an abstract of a report addressed
by Captain Turnbull to Lieutenant-Colonel
Abert, and by him submitted to the House of
Representatives of the United States.
Description of the one-arch Wooden-Bridge, of
205 feet bpan, at Paradenia, with an account of
the execution of the work and the me^ns em-
ployed in throwing it across the river Malia^il-
laganga, in the island of Ceylon. By Captain
Oldershaw, Royal Engineers.
Description of a Series of Bridges erected across
the river Ottawa, connecting the provinces of
Upper and Lower Canada, and especially of a
wooden arch of 212 feet span which crossed
the main branch of the river. By Lieutenant
Denison, Royal Engineers.
Description of a Barometer that requires no cor-
rections either for Zero or for Temperature.
By Samuel B. Howlett, Esq., Chief Draughts-
man, Ordnance.
Notes to aid in correcting the operation of ascer-
taining the Heights of Mountains by means of
Boiling W^ater ; furnished by Major Ord, Royal
Engineers.
On the Decomposition of Metallic Iron in Salt
Water, and of its Reconstruction in a Mineral
form. By Lieut.-Col. Reid, Royal Engineers.
Report on the Effect of Climate on Yorkshire
Paving, communicated by Colonel Fanshawk,
Royal Engineers.
Report of Paving Stables at Brighton.
Experiments tried at Quebec as to the properties
and adhesive qualities of Cements, by order of
Colonel NicoLLS, Commanding Royal Engineer,
dated 17th November, 1834.
Proof of an Earthen Ware Pipe for Lieutenant
Denison. By Mr. Bramah.
Description of a Drawbridge on the London and
Birmingham Railway, at Weedon. By Captain
J ebb, Royal Engineers.
Table of the Description and Weight of the
Packages of various Articles of Traffic. By
Majo^ H. D. Jones, Royal Engineen.
Appendix. — Notes on Lintz.
Notes to pages 36 and 39.
11.
VoL 2, uniform vrith the preceding, Price £1.
12.
Vol. 1, reprinting, Price 15#.
^
-®
13.
1&3 Plates, engraved in the bett ttyle of Ait, half-bonnd, very neat, Price iE4. 4i.
PUBLIC WORKS OF GREAT BRITAIN ;
CONSISTING OF
Railways, Rails, Chairs, Blocks, Cottings, Embankments, Tunnels, Oblique Arches, Viadncli, Bn^
Stations, Locomotive Engines, &c. ; Cast-Iron Bridges, Iron and Gas Works, Canab, Lod-cs&
Centering, Masonry and Brickwork for Canal Tunnels ; Canal Boats ; the London and livenncllt^.
Plans and Dimensions, Dock-gates, Walls, Quays, and their Masonry; Moorlng-cbains, PIib «^
Harbour and Port of London, and other important Engineering Works, with DescripCioos ssd S^-
cations ; the whole rendered of the utmost utility to the Civil Engineer and to the Nobility i^ Gtsr
as Monuments of the useful Arts in this Country, and as Examples to the Foreign Eng;ijieei.
Edited bt F. W. SIMMS, C. E.
This Work is on an Imperial folio size, the Drawings and Engravings have been executed bj esiae
Artists, and no expense has been spared in rendering it highly essential to the Ctvil En^acff ■
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in several Parts of the Kingdom. The Work is bound in half-morocco, there aie some Pistes a^^
Volume that may be prefeired in Colours, viz., the elaborate subject of the Blisworth Cuttia|s,is'
Birmingham Line, 18 Plates, geologically coloured ; Glasgow and Gaimkirk Raflway Cuttiog tkmr
Moss, geologically coloured, &c. ; making 20 Plates, to be carefully coloured, and for w^ ^
additional £1. It, is charged.
The following UalUt qfthe Authort whose worke are conqfrieed m the
Brindley
Brunei
Buck
G. and R. Stephenson
Hartley
Hosking
Jessop
Landmann
M'Adam
Palmer
Rennie
Rhodes
Telford
Thomas
TieraeyCliA
Walker.
14.
22 Plates, large folio, bound. Price £1. U,
THE HARBOUR AND PORT OF LONDON,
SCIKMTIFICALLY, COMMB&CIALLT, AND HISTORICALLY DX8CRIBBD ;
Containing Accounts of the History, Privileges, Functions, and Government thereof; of its S^*
Divisions, and Jurisdictions, Municipal and Commerdal; of its Docks, Piers, Quays, EmbsnbBa*'*
Moorings, and other Engineering Works ; Tidal and other Observations, and every other nectssfj
information relative thereto, accoqipanied by Charts of the Port and its Dependencies, its Sboiis ^
Soundings, surveyed by order of the Port of London Improvement Committee ; Plans of Docici> Gik^
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&c., &c., &c.
By JAMES ELMES, Architect and CivQ Engineer, Surveyor of the Port of Loadoa.
15.
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OUTLINE OP THE METHOD OF CONDUCTING A
TRIGONOMETRICAL SURVEY,
For the Formation of Topogr^>hical Plans ; and Instructions for Filling-in the Interior DetaQ, ^^ •
Measurement and Sketching { Military Reconnaissance, LeveUing, &c., &c ;
With the Explanation and Solution of some of the most nseAil Problems in Geodesy and Tne^
Astronomy ; to which are added, a few Formule and Tables of general utility for £idlitatiog
their calculation.
By Lieutenant FROME, Rotal Enoinbsrb, F.R.A.S., & A.I.C.B.
ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN.
7
16.
RAILWAYS.
In Imperial folio, 83 Engravings, with eiplanatory Text, containing the Specification of the Works as
executed.
Edited by F. W. SIMMS, C.E.
Price £2. I2i, 6d. in half-morocco. — Subjects :
Thb London and Birmingham Railway — ^Thb Giusat Western Railway — The South-
ampton Railway — The Greenwich Railway — The Croydon Railway — The Birmingham
and Bristol Thames Jdnction Railway — Glasgow and Gairnkirk Railway. In 83 Plates,
with Sections, Details, &c.
LONDON AND BIRMINGHAM RAILWAY.
1.
2.
3.
4.
6.
6.
7.
8.
9.
10.
11.
13.
13.
14.
15.
16.
17.
Frontiapiece— London Entfaaee to the PrimroM HOI
Tunnel.
Tide Fttge, rignette— Railwar SUtion at Watford.
Chimney* at Camden Town fixed Engine Station.
Entnuice to Railway Station at Euston Grore — Vig-
nette, page I.
Enaton Grave Station, ground-plan*
Camden Town fixed Engine Station, ground-plan.
Iron Roof— Euston Grore Station.
Stanhope Place and Park Street Bridges.
Brid^ orer the Regent** Canal.
Detail* of ditto.
London and Birmingham Railway — Harrow in the
distance. Vignette, page 17.
London and Birmingham Railway—- Watford Tunnel.
Vignette, page S8.
Road Bridge over Railway.
Colne Viaottct. •
Bridge over Excavation south of Watford Tunnel.
Box Moor Oblique Brid^.
North Chnrdi and Primrose Hill Tunnels — Cross
Secti<ms.
18, I9< Entrances to ditto— Vignettes, pages SI and 84.
SO to SO' Working Section, Bliswortn Kxcavations and
Embankments.
SO, 81. Undersetting of Rock in Blisworth Cuttings — ^En-
larged Scale.
SS, S3. Plan and Elevation of Retaining Walls, Counter-
forts, Inverts, Drains, &c. in the Blisworth Cuttings.
34, 35. General Plan and Section of the Undersetting of
the Rock in the Blisworth Cuttings.
30, 37. Plan, Elevation, and Section of the West End of
the Blisworth Cuttings.
38 to. 47. Plan, Elevations, and Details of the Kflsby Tun-
nel, Warwickshire.
48. Method of fixing the Fifty-pound Rails in the
Chairs.
49. Method of fixing the Sixty-five-pound Rails in the
Chairs.
60. Mr. Buck's Railway Chairs.
61. Plan (rf Siding or Passing Place.
62. Plans and Sections of a 'IVelve-feet Turn Rail.
63. Plan and Elevation of First Class Carriages.
GREAT WXBTBRN RAILWAY.
54. Plan and Elevation of the Brent l^aduet.
55. Sections of the Brent Viaduct.
&6. Transverse Sections of the Brent Viaduct.
57. Plan and Elevation of Maidenhead Bridge.
58. Sections of Maidenhead Bridge.
69. Occupation Bridge over the Bulway.
SOUTHAMPTON RAILWAY.
60. Bridge under Railway.
61. Plan of ditto.
62. Occupation Bridge in Embankment.
65. Oblique Arch over Neekinger Road.
Od. Sections of ditto.
67. OUiqne Arch over Spa Road.
71. New Cross Bridge over Railway.
63. Occupation Bridge.
64. Elevation and Details of Earth-work and Timber
Waggons.
GREENWICH RAILWAY.
08, 09. Sections of ditto.
70. Viaduct of the Greenwich Railway.
CROYDON RAILWAY.
72. Method of fixing the Permanent Way.
BIRMINGHAM AND BRISTOL THAMES JUNCTION RAILWAY.
73. Cast-iron Arch Suspension Bridge over the Paddington 74. Railway Gallery under the Canal, &c.
Canal and the Railway.
GLASGOW AND GAIRNKIRK RAILWAY.
76. Transverse Section at Robroyston Moss.
MISCBLLANBOU8.
i
7O. Comparison of the Transverse Section of numerous
Railway Bars.
77. Comet Locomotive Engine.
78. Mr. Stephenson's Patent Locomotive Engine.
79. Railway Waggons.
80. Flat Rail with Flange.
81. Rail by Losh, Wilson, and BeU.
89. HettonRail.
83. Sidings or Passing Places.
®
8
WORKS PUBLISHED BY JOHN WBALE^
17.
fS^t JlrfD Wiatk an SrOrge Sufllrinf.
Vol. 1, royal octavo, is just completed, Price £1. ]6«., containing 380 pages of Text and 55 elaborately
engraved Plates, with every detail and dimension for practical use, entitled,
THEORY, PRACTICE, AND ARCHITECTURE OF BRIDGES.
The theory by JAMES HANN, of Kino's College,
Hon. Mem. of the Philosophical Society of Newcastle upon Tyne, Mem. of the MathematicaL Sodety
of London, and Joint Author of " Mechanics for Practical Men ;*'
AMD
The practical ENGINEERING and ARCHITECTURAL TREATISE
BY WILLIAM HOSKING. F.S.A.,
Architect and Civil Engineer, Author of ** Treatises on Architecture and Bofldiiig ;''
PROFESSOR MOSELEY, M.A., Kino's College ; T. HUGHES, and ROBERT STEVENSON,
Civil Engineers.
The Work will be completed in 2 Vols., to contain 700 pages of Text, and illustrated by 110 En-
gravings of examples of Stone, Timber, Iron, Wire, and Suspension Bridges, from Drawings furnished
by the principal Engineers of Great Britain and France.
Vol. 2 is preparing, and is to be published in 6 Parts, at intervals, in the course of the year 1840.
\* This Work, when completed, vriU be found to be of a roost valuable character, the highest takat
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AtloM cqpiet qfthe Plate§ may be had.
18.
In demy 8vo., nnmerous Wood-cuts, extra cloth bds., Price 8».
AN ESSAY ON THE BOILERS OF STEAM ENGINES:
Their Calculation, Construction, and Management, with a view to the saving op fukl. Indnding
Observations on Railway and other Locomotive Engines, Steam Navigation, Smoke Burning, Incrus-
tations, Explosions, &c. &c. A New Edition, considerably enlarged and improved.
By R. ARMSTRONG, CivU Engineer.
19.
Vol. 1, Price 30«., extra doth bds., containing a Portrait of the Ute President, Thos. TeUbrd, Esq.,
and 27 finely engraved Plates.
transactions of the institution of ci\aL
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%* Except 15 copies, which only remain of this Volume, all of them being defident of Mr. Macneill's
Tables, the Volume is out of print, and scarce. It will however be reprinted some time in the year
1840.
20.
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TRANSACTIONS OF THE INSTITUTION OF CIVIL
ENGINEERS.
LIST OF SUBJECTS.
Account of the Bridge over the Severn, near the
Town of Tewkesbuiy, in the County of Glou-
cester, designed by Thomas Tklford, and
erected under his su|>erintendence. By W.
Mackenzie, M.Inst.C.E.
-^i*
A Series of Experimenta on diffbcnt kinds of
Amaican Timber. By W. Dbnibon, Ueiit
Royal Engineers, F.R.S., A.Inst.C.£.
On the Application of Steam as a moving Power.
considered especially with tefereaoe to thf
t
ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN.
®
economy of Atmospheric and High Pressure
Steam. By Gsorob Hol worthy Palmer,
M.Inst.C.E.
Description of Mr. Henry Gay's method of giTing
a true Spherical Figure to Balls of Metal, Glass,
Agate, or hard Substances. Communicated by
Brtan Donkin, V.P.ln8t.C.£.
On the expansive action of Steam in some of the
Pumping Engines on the Cornish Mines. By
William Jort Hemwood, F.G.S., Secretary
of the Royal Geological Society of Cornwall,
H. M. Assay-Master of Tin in the Duchy of
Cornwall.
On the effective power of the High Pressure ex-
pansive condensing Engines in use at some of
the Cornish Mines. By Thomas Wickstkbd,
M.Inst.C.E. A letter to the President.
Description of the Drops used by the Stanhope
and Tyne Railroad Company, for the Shipment
of Coals at South Shields. By Thomas £.
Harrison, M.Inst.C.E.
On the Principle and Construction of Railways of
continuous bearings. By John Rbynolds,
A.Inst.C.E.
Wooden Bridge over the River Calder, at Mh^eld,
Yorkshire, designed and erected by William
Bull, A.Inst.C.£.
A Series of Experiments on the Strength of Cast
Iron. By Francis Bramah, M.Iiist.C.£.
On certain Forms of Locomotive Engines. By
Edward Woods.
Account and Description of Youghal Bridge, de-
signed by Alexander Nimmo. By John £.
Jones, AIiist.C.£.
On the Evaporation of Water from Steam Boilers.
By JosiAH Parkss, M.Iiist.C.£.
Account of a Machine for cleaning and deepening
small Rivers, in use on the Little Stour River,
Kent. By W. B. Hats, GTad.Inat.C.E.
Description of the Perpendicular Lifts for passing
Boats from one Level of Canal to another} as
erected on the Grand Western CanaL By
James Green, M.In8t.C.£.
On the methods of Illuminating Lighthouses, wiih
a description of a Reciprocating light. By J.
T. Smith, Captain Madras Engineen, F.R.S.,
A.In8t.C.E.
Experiments on the Flow of Water through small
Pipes. By W. A. Provis, M.In8t.C.E.
Experiments on the Power of Men. By Joshua
Field, V.P.Inst.C.E., F.R.S.
Particulars of the Construction of the Floating
Bridge lately established across the Hamoaze,
between Torpoint in the County of Cornwall,
and Devonport in Devonshire. By Jakes M.
Rendel, M.Inst.C.E., &c. &c.
Appendix. — Officers, Members, &c.
21.
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TRANSACTIONS OF THE INSTITUTION OF CIVIL
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CONTBNTB.
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22.
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TRANSACTIONS OF THE INSTITUTION OF CIVIL
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CONTENTS.
On Steam Boilers and Steam Engines, Part. II.
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On the Comparison between the Powa of Loco-
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1 Plate.
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1838, with Remarks on the Construction of
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let, Colonel R.£., Hon. M.Inst.C.E. 1 Plate.
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as shown by observation on the Southwark and
Staines Bridges. By George Rennie, F.R.S.,
&c. &c.
The Gravesend Pier. By W. Tiernbt Clark,
M.Inst.C.£. 6 Plates.
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Company at their Reservoir in the Hampstead
Road. By R. W. Mylne. 1 Plate.
On Locomotive Engines. By Edward Bury,
M.ln8t.C.E. 4 Plates.
^
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A PRACTICAL TREATISE ON THE CONSTRUCTION AND
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AN APPENDIX,
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rROM NVMBROUB XXPXRIMBNT8 FOR MAKING AN ARTIFICIAL WATBR CBMBNT,
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THE PRACTICE OF MAKING AND REPAIRING ROADS ;
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BOTH STATIONARY AND LOCOMOTIVE ;
And for railways, canals, and turnpikb roads : being a Synopsis of a Course of Eight Lectiar
on MBCHANicAL PHILOSOPHY ; illustntive of the most recent modes of Construction, and an Expoatw:
of the Errors to which Patentees and others are liable, from their not being acquainted with ik
practical departments of Engineering.
By HENRY ADCOCK, CiyU Engineer.
48.
In 5 Parts, large oblong folio, with a Letter-press Description in 4to. to each. Price £1. Is. eecfa Put.
with the Text.
THE CIVIL ENGINEER AND MACHINIST:
PRACTICAL TREATISES OF CIVIL ENOINBBRING, BNGINEBR BUILDING, MACHINBET.
MILL-WORK, BNGINB-WORK, IRON-FOUNDING, &C. &C.
By C. J. BLUNT.
CONTENTS.
«•
Division 1. — Bonlton and Watt's Portable ^team
Engine, complete, with all the details, in 10
Plates.
Division 2. — Marine Steam Engines and Ma-
chinery; Steam Com Mills, &c., complete.
Division 3. — Sugar Mills, on horizontal and verti-
cal construction ; Steam Com Mills, by Mauds-
LAT and FiKLD ; the Kent and Surrey Sewers,
Sluices, &c; Smith's Forge, and Great Forge
Hammer.
Division A. — Sea Entrance Gates, Swing Bridges,
Canal Bridge, Specifications of the Works, &e^
of the Gloucester and Berkeley Canal, Water-
wheels and Iron Rooft, by the late Troma*
Telpord ; Plans, Sections, and Machinery of t>'
Wemyss Colliery, &c
Division B. — Bridges and Viaducts, with tk
original Specifications of the London and Bcr-
mingham Railway, Locomotive and Bogie Es-
gines of do. in detail, the Goods Waggaa5
Tenders, and divers Specifications of Worici
&c. &c., by RoBBRT Stephsnson, Esq. ; L£m>v
motive Engines on the Newcastle and Cari]>-
Railway, by Gsorgb Stephenson, Esq. ; tU
Great Western Railway Bridge, &&, by J. k
Brunbl, F.R.S., &c. &c
9
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ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN. 15
49.
Five Lmaisonf. Plates Atlas fblio» with Text in 4to.
LOCOMOTIVE ENGINBS AND CARRIAGES.
POPULAR FRENCH WORK.
L'Industkib dks Chsmins db Fbr, ou Dessins et Descriptions des Machines Locomotives, des Four-
gons d'approTisionnement (Tenders), Wagons de Transport et de Terrassements, Voitures, Diligences,
lUdls, Supports, Plates-Formes mobiles. Aiguilles, Machines accessoires, &c. &c., en usage sur les
Routes en Fer, de France, Angleterre, Allemagne, Belgique, &c. &c
Par MM. ARMENGAUD.
50.
Second Edition, in 8vo, extra cloth boards, 10 Plates, Price 7«. 6J.
PERSPECTIVE SIMPLIFIED;
Containing a new frkliminart CHApraR, in which the subject is treated in the most plain and easy
manner, for the convenience of readers not acquainted with Geometry.
By Z. LAURENCE, Esq.
51.
In 4to., with Wood-cuts, and 4 fine Engravings by John Lb Kbvx, Price 7t. M.
AN ACCOUNT OP THE ROOF OF KING'S COLLEGE CHAPEL,
CAMBRIDGE.
By F. MACKENZIE, Author and Draughtsman of some of the finest Architectural Works.
52.
In demy 8vo., 3 Engravings, Price 7«. 6<l.
MECHANICS FOR PRACTICAL MEN;
Containing Explanations of the Principles of Mechanics ; the Steam Engine, with its varions Pro-
portions; Parallel Motion, &c. ; Tables of the Weight of Cast-iron Pipes, Strength and Stress of
Materials, &c.
By JAMES HANN, King's College, and ISAAC DODDS, C.E.
53.
4to., Price £\» If. Rerised and corrected.
THE CARPENTER AND JOINER'S ASSISTANT;
Containing Practical Roles for making all kinds of Joints, and yarioos methods of hingeing them
together ; for hanging of Doors ; for fitting up Windows and Shutters ; for the construction of Floors,
Partitions, Soffits, Groins, Arches for Masonry ; for constructing Roofs in the hest manner from a given
quantity of Timher, &c. Also Extracts from M. Belidor, M. du Hamel, M. de Buffon, &c., on the
Strength of Timher. Illustrated with 79 Plates.
By PETER NICHOLSON, Architect.
54.
In 8to., with two large folding Plates of Sections of Roads, Price 2s.
MAKING AND REPAIRING ROADS.
RULES for MAKING and REPAIRING ROADS, as laid down by the late Thomas Tklfoao, Esq.,
Civil Engineer. Extracted, with additions, from a Treatise on the Principles and Practice of Levelling.
By F. W. SIMMS, Surveyor and Ci'v\^ Engi^^^-
16
WORKS PUBLISHED BY JOHN WEAL.E,
55.
4to., with Plates. Price 15t.
A TREATISE ON RIVERS AND TORRENTS,
With the METHOD of REGULATING their COURSE and CHANNELS. By Paul Fmsi, Member
of numerous Academies. To which is added, an ESSAY on NAVIGABLE CANALS, by the same.
Translated by Major-General JOHN GARSTIN.
56.
Wood*cut8, 8vo. Price 5».
SECOND REPORT ON THE LONDON AND BIRMINGHAM
RAILWAY,
Foonded on an Inspection of, and Experiments made on, the LiTerpool and Manchester Railway.
By PETER BARLOW, F.R.S., &c. &c
57.
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AN ESSAY ON THE CONSTRUCTION' OF THE FIVE ARCHl
TECTURAL SECTIONS OF CAST-IRON BEAMS,
Employed as Girdersi Bressummers, and other Horizontal Si^ports for Buildings, &e.
By WILLIAM TURNBULL.
58.
Third Edition. Folio, urith a hirge Athis of Plates. Price £4. 4a.
NAVAL ARCHITECTURE;
Or, the RUDIMENTS and RULES of SHIP BUILDING .- exemplified in a SERIES of DRAUGim
and PLANS ; with Observations tending to the further Improvement of that important Ait. Dedicated
by penniasion, to His late Majesty.
By MARMADUKE STALKARTT, Naval Architect.
59.
Three vols, large 4to., numerous fine Plates. Price £3. 3«.
HISTORY OF MARINE ARCHITECTURE.
By JAMES CHARNOCK, F.S.A.
Illustrative of the Naval Architecture of aU Nations from the eariiest period, particulariy British.
\* Chamock is a work essential to all who study the construction of ships, large and small aJ^
whether for war, packet, or mercantile purposes.
60.
Supplementary and Fifth Volume to the Antiquities of Athena, by R C. Cockerell, Esq., &c.
ANTIQUITIES OF ATHENS AND OTHER PLACES OF GREECE,
SICILY, &c.
Supplementary to the Antiquities in Athens, by JAMES STUART, F.RS.. F.S.A., and NICHOLV^
REVETT; delineated and illustrated by R. C. Cockkrell, RA., F.S.A., W. Kinnard, T. L. DoAir
SON, Member of the Institute of Paris, W. Jenkins, and W. Railton, Architects.
Imperial folio, uniform with the Original Edition of Stuart and Revett, and the Dilettanti Wcri^
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ments, &c. In extra cloth boards aud lettered. Price £G. 12«.
#
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ARCHITECTURAL LIBRARY^ 59^ HIGH HOLBORN.
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61.
Very neatly half-bound in morocco, gilt tops, Price £3. 3».
ARCHITECTURE OF THE METROPOLIS.
DKOICATKD TO lYDNBT SMIEKB, »«., AECHITKCT, V.B.A., V.G.B.
A New and Considerably Enlarged Edition, with many Additional Subjects and Plates, of
ILLUSTRATIONS OF THE PUBLIC BUILDINGS OF LONDON,
In Two Volumes 8vo., with 165 Engravings, origplnally edited by the late Augustus Pugin, Arcliitect,
and John Britton, F.S.A., &c., and now newly Edited and Enlarged
By W. H. LEEDS.
Manifold as are the publications which represent
the various structures of the metropolis, this is
the only work which describes them, not ad libi-
tuntf in views which, even when perfectly correct,
show no more than the general aspect and locality
of each building from a certain point, and conse-
quently afford no information beyond mere ex-
ternal appearance — but exhibits them archtteC'
turaUy by means of plans, elevations, and occa-
sionally both sections and interior perspective
views. Thus a far more complete and correct
knowledge may be obtained of each edifice, in its
entire arrangement in all its parts and dimensions,
than by pictorial views of them.
As studies for the Architect, the subjects con-
tained in these volumes strongly recommend them-
selves,— more particularly so, as of the majority of
them no plans and elevations are to be met with
in any other publication, which materially en-
hances the interest of this collection, and it pre-
serves to us authentic and tolerably complete
records of many buildings which no longer exist.
Among these are Carlton House, illustrated
with several plates, including sections, and a plan
of the private apartments; the late English
Opera House; Mr. Nash's Gallery, which
has since been dismantled of its embellishments ;
and The Royal Exchange.
Among the subjects introduced in this New
Edition will be found the following : — The Tra-
vellers' Club House — London University
— St. George's Hospital — Gateway, Green
Park — ^PosT Ofpice — ^Fishmongers' Hall — St.
Dunstan's, Fleet Street, &c. &c.
62.
Royal 8vo., 18 Engravings, doth boards, 10». 6J.
ILLUSTRATIONS OF THE PUBLIC BUILDINGS OF LONDON,
With descriptive Accounts of each Edifice.
SUPPLEMENT :
Containing the New Subjects and Descriptions by W. H. Leeds, incorporated in the second
edition, and now sold separate for the accommodation of those possessing the first edition.
Also a few copies in imperial 8vo. for large paper copies of the first edition, Price 15«.
63.
In demy 8vo., cloth boards, Price 9t.
A TREATISE ON THE LAW OF DILAPIDATIONS AND
NUISANCES.
By DAVID GIBBONS, Esq., of the Middle Temple, Special Pleader.
Dedicated to the Honourable Sir John Taylor Coleridge, Knt., one of Her Majesty's Justices of the
Court of Queen's Bench.
64.
One large sheet, very accurately coloured, size within the line of work 25^ inches by 18^. Price 10«.
GEOLOGICAL STRUCTURE OF ENGLAND, IRELAND, AND
SCOTLAND.
An Index Geological Map of the British Isles ; constructed from published documents, communications
of eminent Geologists, and personal investigation.
By JOHN PHILLIPS, F.R.S., G.S., Professor of Geology in King's College, London.
Engraved by J. W. Lowry.
Mounted in a case, Price 13#. ; on bhick roller, 16t.*, mahogany do., 18«.
18 WORKS PUBLISHED BT JOHN WEALB^
65.
J
The foIloTving vexy valuable and interesting Work has been withheld from sale for sevcFal years:
the publication price was fixed at £2, 2«., but, as a favourable purchase has been made, the price
is now 16ff. in extra doth boards, and lettered.
A SERIES OF ANCIENT BAPTISMAL FONTS, NORMAN, EARLY
ENGLISH, DECORATED ENGLISH, AND PERPENDICULAR
ENGLISH.
Drawn by F. SIMPSON, Jun., and Engraved by R. ROBERTS.
Large 8vo., contjuning 40 very beautifully engraved Plates, in the best style of the Art, and the Test '
written by an accomplished and talented Gentleman, whose attainments in Architecture and aa an Anti-
quarian are well known and appreciated.
A few copies on large paper, Price £1. 8t. ; and only six copies India prooft, with Etching!, at £2. 2t.
66.
One large 4to. The Plates engraved in the finest style of Art. Cloth boards, lettered, Price £1. lOt.
THE MONUMENTAL REMAINS OF NOBLE AND EMINENT
PERSONS,
Comprising the Sepulchral Antiquities of Great Britain, engraved from Drawings by
EDWARD BLORE, Architect, F.S.A.
With Historical and Biographical Dlustrations.
CONTBNTS.
1. Eleanor, Queen of Edward the Fint. WeainUniter 17. John Q«mw. 8f. 5fltvio«r*« Ckurd^, Somikm^k.^
ilM«y.— 1990. 1408.
8. Effigy of the tame. 18. King Henry the Fourth and hia QneeD. Cmmiertmrf
3. Brian Fitcalan, Baron of Bedale. Bedale Church,^ CathedrtU,—Ul2,
1301. 19. Effigy of Che lame.
4. Aymer de Valenee, Eari of Pembroke. Weaitniruier 80. Thonuw Fitzalan, Earl of Arundd. AnttaM CJhcrcft.
JMcy.— 1334. —1415.
6. Sir Jamea Donglaa. Dowla$ Ckureh.^1931, 81. Ralph Neville, Earl of Wcataaorlaad. Stmm^r^
6. Gervaie Alard, Admiral of the Cinque Porta. Winehel' Church. — 1435.
««a CAurvA.— No date. 88. Arehibald, 5th Bail of Douglaa. Dmtgin G^mrek.^ j
7. Philippa, Queen of Edward the Third. WeutmihuUr 1438. 1
Abbey. — 1360. 83. Richard Beauchamp, Earl of Warwi^
8. Effigy of the lame. Chapel, Warteiek.— 1439
0. Thomaa Beauchamp, Earl of Warwick. Bemiehatnp 84. Effigyof the tame.
Chapel. Warurick.^1970, 85. John Beaufort, Duke of SomerBOt. Wimharm MmUer.
10. Edward, Prince of Walea. Canterbury Cathedral.-^ —1444.
1370. 86. Humphrey, Duke of Olonceater. St, AWam*e JUcy.—
11. Effigy of the same. 1446.
13. King Edward the Third. Weatmimier Abbey.— 1377- 37. Sir John Spencer. Brington CAtirdh.— 1588.
13. Effigy of the name. 88. Archbiahop* Warham and Peckham. Camierbmy
14. Thomas Hatfield, Biahop of Durham. Durham Cathe- Cathedrat.—\i32.
dral. — 1381. 99. Margaret Plantagenet, Goonteia at
15. William of Wykham, Biahop of Winchester. Win- Church, Hampthire.—lSil.
eheeter CaihedraL-~\ilH» 80. Sir Anthony Bxtmne. BaiU
16. Effigy of the same.
80. Sir Anthony Browne. BoMeilMqr.— IS48.
67.
In folio size, Price ;61. \$, in hoards.
BRIDGEN'S INTERIOR DECORATIONS, DETAILS, AND VIEWS I
OP SEFTON CHURCH, IN LANCASHIRE,
Erected hy the Molineox family (the ancestors of the present Earl of Sefton), in the early part of the
reign of Henry VIII.
The Plates (34 in nnmber) display the beautiful Style of the Tudor Age in Details, Ornaments, :
Sections, and ViewB. Etched in a masterly style of Art. |
%
ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN.
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68.
Royal 4 to., very neatly half-bound in morocco, gilt. Price £2. I2s. 6d.
DRAWINGS OF THE FINEST EXISTING SPECIMENS OF
ANCIENT HALF-TIMBERED HOUSES OF ENGLAND,
And of their Details ; with an Essay, showing the Classification of the Style, and the Age to which it
belongs.
By M. HABERSHON, Architect.
%* The work contains upwards of Twenty Views, taken from the finest remaining Specimens of this
interesting branch of the Ancient Architecture of England, comprising Manor Houses, Town Resi-
dences, and Cottages, some of which are particularly striking and picturesque ; and, in order to give a
more complete illustration of it, such Views are accompanied by Drawings, to a large scale, of Chim-
neys, Tracery, Porches, Doors, Windows, and other Details. To which is added, an Essay, giving a
General Historical View of English Architecture.
69.
With Plates, imperial 8vo., cloth boards, £1. 1».
CLARKE'S ELIZABETHAN ARCHITECTURE.
Wimbledon Honse, Suxrey, built by Sir Thomas
1588.
Easton House, Esiicx, Sir Henry Majmard.
AKton Hall, Warwickshire, Sir Thomas Holt.
Grafton Hall, Cheshire, Sir Peter Warburton.
Stanfield Hall, Norfolk, family of Flowerdews.
Seckford Hall, Thomas Seckford.
Bramshill House, Hampshire.
Fenn Place, Kent, Lord Zouch.
Queen's Head, Islinpton, Sir Walter Raldgh.
ChasletOD, Ozfordahure, Walter Jones.
CONTENTS.
Cecil, Brereton Hall, Clieshire, Sir Walter Brereton.
Holland House, Middlesex, Sir Walter Cope.
Haughley House, Suffolk.
Streete Place, Sussex, Dobell.
Montacute House, SomersetsluTe, 8ir Edward FliiUpa.
Westwood House, Worcestershire.
Wakehurst Place, Sussex, Sir Edward Culpeper.
Carter's Comer, Sussex.
Eastbuiy House, Essex, Lord Monteagle.
East Mascall, Sussex, Newton.
Old House, near Worcester, &c.
70.
Sixty Plates, Title-Page printed in colours and gold, el^^^^^^y half-bound in morocco, and lettered,
Price £1. 16«.
SPECIMENS OF THE ARCHITECTURE OF THE REIGNS OF
QUEEN ELIZABETH AND KING JAMES L,
From Drawings by Charles Jambs Richardson, Gborob Moorb, and other Architects, with
Observations and Descriptions of the Plates.
Eighteen Plates iUustrate the Old Manor House, the Gardens, Terraces, &c. at Claverton, the Seat of
George Vivian, Esq. — six the Duke of Kingston's Picturesque House at Bradford — and eight the
princely Mansion of Lord Holland at Kensington.
The volume contains examples of Ceilings, Porches, Balustrades, Screens, Staircases, Monuments,
Pulpits, &c. ; and a rich collection of Facsimiles of Old English Drawings, chiefly of John Thorpe,
the most eminent Artist in Qaeen Elizabeth's time.
71.
In 8vo., extra cloth boards, and lettered, Price 7«. — 25 copies are printed on India paper, Price lOt. M.
Second Edition, corrected.
HAKEWELL'S ATTEMPT TO DETERMINE THE EXACT
CHARACTER OF ELIZABETHAN ARCHITECTURE,
Illustrated by Parallels of Dorton House, Hatfield, Longleate, and Wollaton, in England ; the Pallazzo
della Cancellaria, at Rome.
The Plates (8 in number) consist of compartments of the Pallazzo della Cancellaria, at Rome, by
Bramante, 1495; and Longleate, by John of Padua, 1547. Compartment of the South Front of
Hatfield, 1611, with comptftroent of WoUaton Hall, 1580; Dorton House, Bucks — a Plan, Screen in
-%
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20 WORKS PUBLISHED BY JOHN WEALB^
the HaU ; Longitudinal Section of the Staircase ; Transrene Section of the Staircase ; ChimiieT-piece
in Queen Elizabeth's room ; Ceiling in the same room ; a front view of the Queen occupies the centre
compartment ; the corresponding compartments are filled with the Portraits of her principBl Blinisters
in profile.
72.
8vo.| cloth boards, and lettered, Price S$. '
MOLLER'S GERMAN GOTHIC ARCHITECTURE,
Translated With Notes and niustrations by W. H. LEEDS.
73.
In 8vo., with Notes and Illustrations by W. H. LEEDS. Price £4. 4#.
German Satbic ^SLxtbittctavt.
MEMORIALS OF GERMAN A-RCHITECTURE;
Or, the ARCHITECTURAL ANTIQUITIES OF GERMANY.
By GEORGE MOLLER, of Darmstadt, Architect to the Grand Duke of Heaae.
2 vols., large folio, with 130 Plates, a Description of each Edifice, and an Essay on the Origin and Pro-
gress of Gothic Architecture, with reference to its Origin and Progress in England ; in the German
Language, accompanied by an English Translation.
' The Tnuitition, or Early German, haa not yet« ao far more will probably appear in a abort time. Dr. MoDer't
aa I knoWj receired much matinct attention. Dr. MoUer, work (Denkmaehler der Deutachen Banknnat) alraadT coo-
however, in the course of hia valuable Denkmaehler, baa tains excellent specimens of every style of German bniU-
recentlv given na excellent representations of the Cathedral inga, and offera additional intereat and bcanty in _„
at LimbuTj^, on the Lahn, which ia a very admirable sped- number.' — Whewell's Notes on German Chuvdies, pp.
men of thia kind ; and has noticed the intermediate and 28, 20.
transition place which this edifice seems to occupy in the * The Church of St. Catharine, at Oppenbcim, near
developement of the German atyle.' — Whewell's Notes on Worms, also in part a ruin, ia another fine example of this
German Churches, p. 25. style, and has been worthily illustimted in the mafptificent
' There exist, however, several valuable pnblicationa, with work of Dr. MoUer.' — Whewell'a Notea on Gcroua
good pJatea, on the sul^ect of German Architecture, and Churches, p. 113.
Sereral copies of Seventy-two Plates, making Vol. I., have been sold in this country : some copies of
the 2nd Vol. to make up these sets can be had for £2, 12«. 6J.
74.
Royal 4to., with Plates. Price £1. U.
PROLUSIONES ARCHITECTONICiE ;
Or, ESSAYS on Subjects connected with GRECIAN and ROMAN ARCHITECTURE. Dlostrated br
Forty Engravings by eminent Artists. Dedicated, by permission, to Eabl Grst, ILG.
By WILLIAM WILKINS, A.M., R.A., P.R.S.,
Formerly a Senior Fellow of Caius College, in the University of Cambridge ; Professor of Ardiitectare
in the Royal Academy of Arts.
75.
2 vols 4to., upwards of 70 Plates and Wood-cuts, Price £2. 2f.
LETTERS OF AN ARCHITECT FROM FRANCE, ITALY,
AND GREECE;
Or, CRITICAL REMARKS on CONTINENTAL ARCHITECTURE, ANCIENT and MODERN, and
on the CLASSIC ARCHITECTURE of GREECE. Written in a Series of Letten.
By JOSEPH WOODS, F.A.S., F.L.S., F.G.S., &c
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76.
8vo.» with Plates, Price 7#.
VENTILATION, WARMING, AND TRANSMISSION OP SOUND.
REPORT OF THE COMMITTSB OF THE HOUSE OF COMMONS ON VENTU^TION, WARMING,
AND TRANSMISSION OF SOUND,
Abbreviated, with Notes. By W. S. INMAN, Architect, F.I.B.A.
77.
In 8vo., illustrated with a very fine Frontispiece of St. Paul's Cathedral, by Gladwin. Extra
cloth boards. Price 10«. 6 J.
THE PROFESSIONAL PRACTICE OF ARCHITECTS AND THAT
OF MEASURING SURVEYORS,
And Reference to BUILDERS, &c., &c., from the time of the celebrated Earl of Burlington.
By JAMES NOBLE, Architect, F.I.B.A.
78.
78 very fine Plates, royal foHo, neat in cloth boards and lettered, Price £3. 3#.
THE UNEDITED ANTIQUITIES OF ATTICA.
By the Society of DilettantL Comprising the Architectural Remains of Eleusis, Rhamnus, Sunium,
and Thoricus.
79.
8vo., with Plates, Price 7«.
COTTAGES AND HOUSES FOR THE PEASANTRY AND
EMIGRANTS.
ELBMBNTART AND PRACTICAL INSTRUCTIONS ON THB ART OF BUILDING COTTAGES AND HOUSES
FOR THE HUMBLER CLASSES.
An Easy Method of Constmcting Earthen Walls, adapted to the Erection of DweDing-hoiises, Agri-
cultural and other Buildings, surpassing those built of Timber in comfort and stability, and equalling
those built of Brick, and at a considmble saving. To which are added, Practical Treatises on the
Manufacture of Bricks and Lime ; on the Arts of Digging Wells and Draining ; Rearing and Managing
a Vegetable Garden ; Management of Stock, &c. For the use of Emigrants ; for the better Lodging <2
the Peasantry of Great Britain and Ireland ; and the Improvement of those Districts to which the
benevolence of Landed Proprietors is now directed.
By WILLIAM WILDS, Surveyor.
The work contains : —
Chap. I. The Art of Conttruetinff Houms and Cottages IV. On the Propertiei, Usee, and Manufuture of lime,
with Earthen Walla nuule easy, being^ intellinble to all V. On Well-dining, Draining, WeU-ainking, ftc. ; on
claaaes, and to the moat ignorant m building, with Fuel, on Oardening ; what quantity of Land will keqp a
Wood-cttta of tools, plans, and sections, &e. Family in culinary VM;etables ; Fork, Ens, Milk, and
II. On Bricks, how they are to be advantageoualy applied Bread Com ; on the Keeping of Gowa, Hogs, Ponlt^,
in conjunction with rammed earth ; rules for selecting Beea, and Art of making of Candles, So^, Storing Fruit,
tiie best earth, &c. Roots, &c.
III. On the Manu&cture and Choice of Bricks.
80.
In 4to. Plates, very neatly coloured, cloth boards and lettered, Price 16«.
A SERIES OF DESIGNS FOR VILLAS AND COUNTRY HOUSES,
Adapted with Economy to the Comforts and to the Elegances of Modem life, with Plans and
Explanations to each.
By C. A. BUSBY, Ar^hi^^
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81.
Second Editioiii 4to., Price £1. It.
DESIGNS FOR VILLAS AND OTHER RURAL BUILDINGS.
By the late EDMUND AIKIN, Architect.
Engraved on 31 Plates, with Plans and Elevations, elegantly coloured, and an Introductory Essay,
containing Remarks on the prevailing Defects of Modem Architecture, and on the Investigation of the
Style best adapted for the Dwellings of the Present Times. Dedicated to the late Thomas Hope, Esq.
' Modem Architects profess to imitate anticme examples, which is superior to the details that poide them? This is
and do so in colmnns, entablatures, and detaus, but never a subiect which it may be useful and mterestiDg to puxvoe.'
in the general effect. Is it that they imitate blindly, and — Vide Introduction,
without penetrating into those pxinciples and that system
82.
16 Plates, large 4to., Price I6s.
DESIGNS FOR RURAL CHURCHES.
By GEORGE E. HAMILTON, Architect.
83.
Second Edition, in 8vo., iUustrated with numerous large folding Plates, Price 12#. 6J.
A POPULAR TREATISE ON THE WARMING AND VENTI-
LATION OF BUILDINGS,
Showing the advantages of the Improved System of Heated Water Circulation, &c. &c. &c.
By CHARLES JAMES RICHARDSON, Architect
84.
The Sixth Edition, Price 18«. bound.
THE PRACTICAL HOUSE CARPENTER, OR YOUTH'S
INSTRUCTOR ;
Containing a great variety of useful Designs in Carpentry and Architecture ; as Centering for Groins,
Niches, &c. ; Examples for Roofs, Skylights, &c. ; Designs for Chimney-pieces, Shop l^nts. Door
Cases; Section of a Dining-Room and Library; variety of Staircases, with many other important
Articles and useful Embellishments. The whole illustrated and made perfectly easy by 148 4to.
Copper-plates, with Explanations to each.
By WILLIAM PAIN.
85.
In small 8vo., for a Pockel-Book. A New Edition, with the Government Tables of Annuities.
Price 79, boards.
TABLES FOR THE PURCHASING OF ESTATES,
Freehold, Copyhold, or Leasehold, Annuities, &c, and for the Renevring of Leases held under Cathedral
Churches, Colleges, or other Corporate Bodies, for Terms of Years certain, and for Lives ; also, for
valuing Reversionary Estates, Deferred Annuities, Next Presentations, &c. Together with several
useful and interesting Tables connected with the subject. Also, the Five Tables of Compound Interest.
By W. INWOOD, Architect and Surveyor.
86.
12mo., Price 3». 6<f.
A MANUAL OF THE LAW OF FIXTURES-
By DAVID GIBBONS, Esq., of the Middle Temple, Special Pleader.
%* A work purposely written for the use of Builden, House Agents, and House and Land Proprieton.
9 «
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ARCHITECTUBAL LIBRARY^ 59^ HIGH HOLBORN. 23
87.
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THE BUILDING ACT (at Large), side References.
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89.
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By SIR HUMPHREY DAVY, Bart.
90.
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A TREATISE ON ISOMETRICAL DRAWING,
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Engineering; with Deteuls of improved Methods of preserving Plans and Records of Subterranean
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By T. SOPWITH, M.I.C.E.
91.
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A SET OF PROJECTING AND PARALLEL RULERS,
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92.
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GEOLOGICAL SECTIONS
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93.
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WORKS PUBLISHED BY JOHN WEALE^
94.
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OBSERVATIONS ON THE CONSTRUCTION AND FITTING UP
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FURNITURE AND INTERIOR DECORATIONS.
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CHIPPENDALE'S 133 DESIGNS OF
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96.
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SPECIMENS OF THE CELEBRATED
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97.
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CHIPPENDALE'S DESIGNS for
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98.
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DESIGNS FOR VASES, on 17 Plates.
99.
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100.
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A BOOK OF ORNAMENTS, suitable
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Carver.
101.
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ETCHINGS, representing the BEST
EXAMPLES of ANCIENT ORNAMENTAL
ARCHITECTURE, drawn from the Originals
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NAMENT. By C. H. TATHAM, Architect,
102.
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ORNAMENTS DISPLAYED, on a fall
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103.
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DESIGNS OF VALANCES AND DRA-
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This work contains a variety of Yalanoes and
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As a limited number of this work is prepared,
orders are requested as eariy aa possible.
104. <
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ORIGINAL DESIGNS FOR CABINET '
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ORIGINAL DESIGNS FOR CHAIRS J
and SOFAS, vnth MUSIC STOOLS, FOOT ,
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T. KING. ,
106.
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THE UPHOLSTERER'S SKETCH- ■
BOOK OF ORIGINAL DESIGNS FOR
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107.
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THIRTY-SIX NEW. ORIGINAL, AND
PRACTICAL DESIGNS for CHAIRS, adapted
for the DRAWING and DINING-ROOM.
PARLOUR and HALL. By W. TOMS, junior,
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«
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ARCHITECTURAL LIBRARY^ 59^ HIGH HOLBORN.
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108.
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whole £2. 2s.,) containuig 84 Plates.
AN ENTIRE NEW SERIES OF
CABINET AND UPHOLSTERY DESIGNS,
intended to embrace eyery variety of elegant
and useful Furniture, suited to the Palace or
Cottage, including the various styles of Greek,
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SMITH.
109.
Price £1., 4to. post, common paper, 15»., contain-
ing 37 Phites, and 44 pages of letter-press.
UPHOLSTERERS' ACCELERATOR,
Being Rules for Cutting and Forming Draperies,
Valances, &c,, accompanied by appropriate Re-
marks, and containing a full description of a New
System, which will greatly facilitate and improve
the execution. By T. KING.
110.
On 80 Plates, conveniently small for the pocket,
Price £1. 3«.
DECORATIONS FOR WINDOWS
AND BEDS.
I Consisting of 100 Fashionable Designs for Uphol-
I stery Work, with the Varieties of the present Style,
divided into parts. By T. KING.
111.
; Price 15*. coloured, containing 21 Plates, 4to.
j demy, half-bound.
MODERN DESIGNS FOR DRAPERY
AND VALANCES.
Displayed in Beds and Windows.
By T. KING.
112.
Just published, 3 Parts, Price £1. 10*.
WORKING ORNAMENTS AND
FORMS,
Full size, for the ase of the Cabinet Manufacturer,
Chair and Sofa Maker, Carver, and Turner.
By T. KING.
113.
2 vols., large 4to., 60 Plates, Price £2. 5«.
CABINET-MAKERS' SKETCH
BOOK. By T.KING.
114.
Price £L
SUPPLEMENTARY PLATES
To the work entitled "The Modem Style of
Cabinet Work Exemplified in New Designs.^'
By T. KING.
The Supplementary Plates consist of 68 New
Designs, on 28 Plates.
115.
Price £2., mediom 4to., half-boimd; common
edition, £1. 12«. in boards.
THE MODERN STYLE OF CABINET
WORK EXEMPLIFIED IN NEW
DESIGNS,
On 72 Plates, contsining 227 Designs for Cabinet
Work. By T.KING.
116.
Price £1., 42 Plates, on royal 4to., many of which
are neatly coloured.
DESIGNS FOR CARVING AND
GILDING,
With Original Patterns for Toflette Glasses.
By T. KING.
117.
Price 5»., 8vo.
R. MAINWARING'S CHAIR-
MAKERS' GUIDE.
200 Genteel Designs (1766).
118.
Large 8vo., Price 7«.
HOUSEHOLD FURNITURE.
In the taste of a century ago, containing upwards
of 350 Designs on 120 Plates.
119.
Price 15«., 18 Plates, on folio demy.
SHOP FRONTS AND EXTERIOR
DOORS,
Displaying the most approved of London execu-
tion, and selected aa bdng those of the best taste
and greatest variety ; drawn to a scale by accurate
measurement accompanied by the proper Sections
and Plana, with several l^ew Pracdod Dengns :
for the uae ^f tb^ Architect, Builder, and Joiner.
By T. KIJ^^'
26
WORKS PUBLISHED BY JOHN WBALE^
120.
Omamentil*
GRECIAN ORNAMENTS.
A SERIES of EXAMPLES, in 21 Plates, of GRECIAN ORNAMENT, in royal folio, tot M
engraved from Dravdngs made by the most celebrated Architects. I^ce lbs,
CONTENTS OF THE WORK*
Restored Elevmtion to the Entnnce of tbm Sohtatarn
Chambers at Mjceam, oonunoolj called tlie TteaMr J
Atreus.'
Marble Stele, in the poMesaion of Mr. Gropina, at Atka^
Terracotta Antefiza, at Athena, and MacUc Frapva
from I>elphi.
ISIaater Capitals from Stratonice and HalienmaaaBt.
Fragments from Halicamassus, Teoa, and Teaiple i
Apollo, at Branchydte, near MQetoa.
Entasis of the Columns of the Portico of the Prap^Ict-
of the North Wing of the Propylsea.
of the Temple of llieseus.
of the Temple of Minerra, or Parthenon.
of the Chonigic Monument of LjsicEates.
of the Columns of the NorUi Portico of the T-,-
Temple, termed the Erecbtheum.
of the Columns of the East Portieo of that Tes;«
of Ae Temple of Jupiter PanheUeaiua, at .Cf.e.
of the Columna of the Prooaos of the »>:
Details of the Ceiling of the Prapylaa, at Eleusia.
Order of the Antae ofthe Inner Vestibules, at Elensis.
Capital of the Antse at lar^, at Eleusis.
Fragments found at Eleusu.
Tiles and other Details of the Temple of Diana Propyliea,
at Eleusis.
Capitals and Profile of the Temple of Nemesis, at Rham>
nus.
Ornamental Moulding, Jamba, Mouldings of Interior Cor-
nice, the Painted Bf ouldings of the F^eis of the Lacu-
naaia, &c. &c. of the Temole of Nemesis, at Rhamnus.
Details of the Roof, Tiling, oec. of the Temple of Nemesis,
at Rhamnus.
The Chairs and Sepulchral Bas-reUe& found in the Cella of
the Temple of Tnemis, at Rhamnus.
Athenian Sepulchral Marbles, Capitals, and Triglyphs, at
Delos.
Entablature of the Order of the Pejistyle and Roof, Orna-
ments, &c. of the Temple of Apollo Epicurus, at Bassee.
Details of Sculptured and Painted Shafts of Columns of the
Subterraneous Chamber, at Mycenae.
Temple.
This work is very desirable for Sculptors, Modellers, Masons, (in designing for Monuments, Tor'
Tablets, &c.) Builders, and Architects. Those who possess the Dilettanti work of the Vnei^J
Antiquities of Attica, and the Supplementary volume of Antiquities of Greeoe, Sicily, Jcc, will doc zh^
this work, as the subjects are selected from them.
VALUABLE ENGRAVINGS ON ARCHITECTURE, CIVIL AND
MECHANICAL ENGINEERING.
121.
LONDON BRIDGE : engraved on Steel,
in the best style, by J. W. Low&y, under the
direction of B. Albano, Esq., C.E., from his
Drawing presented to the Institution of Civil
Engineers, and made from the Original Draw-
ings and Admeasurement, vnth permission of
ISir John Rennie, F.R.S., the Engineer. 1st.
Part. Plan and Elevation on a large scale, 25
feet to 1 inch. lbs. On India Paper, £1. Iff.
122.
STAINES BRIDGE : a fine Engraving
by J. H. Lb Keux, under the direction of
B. Albano, Esq., C.E., from his Drawing pre-
sented to the Institution of Civil Engineers,
and made from the Original Drawings and
Admeasurement, with permission of George
Rennie, Esq., F.R.S., the Engineer. 1st. Part.
Plan and Elevation on a scale of 10 feet to
1 inch. lOff. On India Paper, lbs.
123.
PARIS — Bridge of JENA, 2 fine Prints.
Plan, Elevation, Section, and Details. Draw-
ings made by L. Golembrowski, C.E. (Polish
Engineer residing in Paris), from admeasure-
ment, by permission ofthe French Government.
lOff.
124.
GLADWIN'S Fbe Engraving of ^
Patent Self-Acting Slide Lathe, manufacrj*
by Messrs. J. WHrrwoRTH and Co., M^
Chester. 5ff. India paper, 7». 6d.
125.
GLADWIN'S Fine Engraving of a Drl
ing and Boring Machine, by Mesaia. Wu.
WORTH and Co., Manchester. 7s.
126.
GLADWIN'S Elevation of Stbphkn»»
Patent Locomotive Engine, printed on Vi
paper for colouring. Columbier aize. 3«. 6«
127.
GLADWIN'S Splendid EngraTing
Stephenson's Patent LocomotiTe Eogiue.
Large folio, Price 7s.
%* This is a master-piece of Mechanical '
graving, and may be considered unique it
execution.
128.
Lithographed Folio Print of the Vcr
brated Train Carriage for Railways, to disti
Friction and Concussion. Mr. B. .Vp>
Patentee. 2s.
ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN.
27
129.
Price £1. 8«.
LERRISSEAU'S Fourteen Plates of
Engravings, on a large Atlas folio size, of the
following, being a set.
Arch of PoU in Istria.
Arch of Traian.
Temple of PoU in Istria.
Temple of Venus.
Amphitheatre of Capua.
Inside of the Temple of Concord.
Ancient Sepulchre situated in Naples.
Arch of Septimus Severus and of Caracalla.
Amphitheatre of BeneTentum.
Temple of Serapb.
Tomb of Virgil.
Temple of Jupiter Statof .
Temple of Antoninus and Faastina.
Gate of Ciuna.
130.
Gilt frames and glazed, very neat, llff. the pair.
PORTRAITS FRAMED AND GLAZED
FOR AN OFFICE.
A Pair of Portraits of Geo. Stephenson, Esq.,
of Newcastle upon Tyne, and Robert Steven-
son, Esq., of Edinburgh, Civil Engineers.
131.
Handsomely engrayed on Steel, (size 16 inches by 10^ inches,) Price 2«. 6d. plain, 3«. coloured.
A CHART OF THE HARBOUR AND PORT OF
LONDON,
iliibiting the River Thames and the adjacent Docks from London Bridge to Bugsby's Hole, and
eluding the Greenwich Railway, the Commercial Railway, and the commencement of the Croydon
ilway.
In this Chart the Low-water Mark, Soundings, Shoals, and other important features, are inserted
tm the most recent surveys ; and, from the care which has been exercised in indicating correctly thti
nous Mfliarfs, Dock-yards, Warehouses, and Factories, on each side of the River, it will be found of
i&i utility to all persons engaged in nautical or commercial pursuits.
SIR CHRISTOPHER WREN'S
ARCHITECTURE.
SS. Plan of hia First Design of St. Paul's, U.
33. Elevation and Section of Bow Church, 1«. 6tf.
34. Interior of St. Stephen's, Walbrook, U.
35. Section of St. James's Church, PiccadiUy, 1«.
36. Roof of the Theatre at Oxford, l«.
37. Plan for the Rebuilding of the City of London, U.
38. Elevation, Plan, and Section of the College of Phy-
ans, London, 1«. 6d.
39. Elevation of the Tower and 8pii« of St. Dunstan's
::be East, London — ^Elevation and Section of Chichester
xe, l«. 6d.
140.
WESTMINSTER HALL.
Section from admeasurement by Mr. George Allan,
(Clerk of the Works to Sir Robert Smirke, Architect to the
late Renovation). Very neady engraved by Mr. Hawks-
WOBTH. Folio sixe, 2t. (id.
141.
SECTION OF ST. PAUl's CATHEDRAL.
ThK OaiOINAL SrLBTTDID ElfOBAYINO by GWYN, of
the Section of St. Paul's CATHanaAi., decorated
agreeably to the original intention of Sir Christopher
Wren; a very fine Urge Print, showing distinctly the
construction of that magnificent Edifice. Price lOi.
This is a magnificent Plate, the only one of its kind,
showing constructively the genius of Sir Christopher Wren.
The follonnng Prints, 8vo. size, are 6J. each ; 4to. size, on India paper, 1«. each.
47.
48.
i9.
30.
51.
42. Mr. Greenough's Villa. 2. D. Burton.
43. Catholic Chapel, s. Newman.
44. York Stairs' Water Gate. 1. I.Jones.
45. Somerset House, (Elevations, Interiors, aodViewt).
Chambers.
46. Society of Arts. I. Adam.
CKillcge of Physicians. 2. Wren.
Newgate. 1 . Dance.
Church of St. Peter le Poor. 1. Gibson.
East India House. 1 . Jupp.
Ashbumham House. 2. 1. Jones.
52. Church of St. George. 3. Hawkamoor.
53. Church of All Souls. 1. Nash.
54. Westminster Hall. 9. Nash.
55. Banqueting House. 1. I. Jones.
50. Mansion House. 1. Dance, &c.
57. County Rre Office. 1. Abraham.
58. University Club House. 1. Wilkins and Gandy.
59. Tower of Bow Church. 1. Wren.
60. Westminster Abbey Church. 0. Wren.
61. Hall, Christ's Hospital. I. Shaw.
62. Carlton Palace, fl. Sir R. Tavlor.
G3. College of Physicians and Umon Club House. S.
R. Smirke.
164. Terraces in the Regent's Park. 9. Nash and D.
Burton.
Ids. Council OiBce, ftc. 1. Soane.
106. Bank of England. 3. Soane.
167. Law Courts, Westminster. 3. Soane.
168. House of Lords, &c. S. Soane.
169. Colosseum, Regent's Park. 1. D. Burton.
170. Hanover Chapel. 1. CockereU.
171. Temple Bar. 1. Wren.
172. House of Mr. Nash, &c. 2. Nash.
17s. Belgrave and Eaton Squares. 2. Nash.
174. Mr. Kemp's Villa. 2. Kendall.
175. London, Southwark, and Waterloo Bridges.
Bennie.
176. Bridge of Blackfnars. 1. Mylne.
177. Bridge of Westminster. 2. Labelye.
178. King's Entrance, House of Lords, Section and In-
terior Views. 8. Soane.
170' Plan and Interiors of St. Stephen's, Walbrook. 2.
Wren.
180. Plan and Interiors of Temple Church. 3. Wren.
181. Plans, Elevation, and Section of Custom House,
London. 2. Laing.
189. Plan and Elevation of Uxbridge House. Vardy.
6.
#
183. PUns, Elevations, Vmwb, and Seckuma of St. Paul'a
Cathedral. 8. Wxen.
184. Elerations and Seetioni of St. Maxtin't Choxcli. 8.
Gibba.
185. Flan, Section, and Ele¥ati<m of the Qiieen*t Theatre.
S. NMh and Repton.
186. Flan and Elevation of the Diorama. Piigin and
Morgan.
187. Flan, Elevation, and Interior View of Haymarket
Theatre. Nuh.
188. Flan, Side Elevation, and Interior of Weetminster
Abbey. 2.
189. Flan, Elevation, Section, and Interior of St. Mary
Woolnoth. 2. Hawknnoor.
100. Flan, Elevation, and Section of St. F1ulip*t, Regent
Street. 9. Rmton.
101. Flan ana Elevation of Bethlem Hoepital. Lewis.
iga. Flan and Elevations of Burlington Hoose. Lord
Burlington and Colin Campbell.
103. Elevation and Secti<ms of St. Bride's Choreh. S.
IK^ren.
104. Interiors of Sir John Scene's House. S. Soane.
105. FLan, Elevation, and Section of St. Paul's, Covent
Garden. Iniso Jones.
106. Elevation of the Royal Exchange. 9. Jeiman.
107. Flan and Elevation of the Russell Institution.
106. Interiorofthe Mansion of Thos. Hope, Esq. a. Hope.
100. Flan, Elevation, and View of the library of the
London Institution. 9. Brooks.
900. Flan, and Transverse and Longitudinal Sections of
King Henry Tth's Chapel. 9. Begun 1509.
901. Flan, Elevations, Interiora, and Seetioia
Garden llieatre. 6. Sir Robert Smirke.
909. Flan and Elevation of Sir John Naah'an
90S. Flan and Transverse Section of St. Jaataca'a^
dilly. Wren.
904. Interior of Freemasons' Hall. Sandbr.
905. Flan, Elevation, and Sections of St. JLoke'a
Chelsea. 9. Savage.
906. Elevationa, Seetiona, and Plan of St.
Church. 8. Inwood.
907. FUn and Elevation of All Sainta GbmcAi,
HoUis.
908. Elevation and Section of St. Dnnsten'a m Oe
Wren.
900. Elevation and Section of Bow ChmA. ITia
910. Flan and Elevation of St.
Hardwidw.
911. Flan, Sections, and Interior of tlM
Chiqpel, Moorflelds. 8. Newman.
919. Flan, and Garden F^ont of the British
(Old). Fouget.
9IS. Flan and Elevation of the Horse Gimvda.
914. Flan and Elevation of the Villa of Ji
Esq. Burton.
915. View of the East side of Belgravna S<iaaK.
916. Flan, View, Sections, and Intetiora of
Tlaeatre. 6. B. Wyatt.
917. View of the Interior of the English Opcfa
Beasley.
918. View of the Interior of the AmphitficBfif ,
minster Bridge.
910. View of the Five Elliptical Arch Bridge across the
Tweed at Kebo. Constructed by the late John Rennie,
Esq., Civil Engineer. Laxf^ print, 5«.
990. View of the Centering of Blackfriars' Bridge, by R.
Mjrlne. Engraved by the celebrated FiranM. Large
prmt, 4«. 6d,
991. View of the Progress of the First Arch of New
London Bridge, with Centering, U. 6<l.
999. View of the Menai Suspension Bridge. By W. A.
Frovis, Esq., C.E., &c. Fine large print, India, 10*.
993. View of the Cast Iron Bridge across the Galton
Canal. By R. Bridgens. Laxf^ sise, 4«. 6tf. India proofs, 6t.
994. View of Hammersmith Suspension Bridge. Finely
engraved, large sise. 5s.
995. Flan and Elevation of Shrewsbury Bridge, Is. 6rf.
996. Dr. George Meier's very Elaborate Detailed Plates
of the Cathedral of Cologne, on nine very large sited sheets,
showing the minutest detail to a large scale: this very fine
structure is nearly coeval with St. Stephen's Chiq^, Glas-
gow Cathedral, and other Edifices of the best age of Archi-
tecture in this Country. With a test, small folio, in the
Goman language, 4^4. 4«.
997. Mr. Britton's Views of the West Fronts of 14
English Cathedrab, fdio sise, 8t. ; aequatinted, 10*. 6tf.
998. Mr. Britton's Series of Picturesque Views of the
Interior of 14 Cathedrals, with a Border of Architectural
and Sculptural Ornament, folio sise, 8c.
990. Vsrdy's Perspective View of the Gothic Hall,
Hampton Court, finely engraved, folio, 5s.
930. Mr. Coney's View of the Interior of the Cathedral at
Miiui, fine large print, 6f.
931. Geometoical Elevation of the Wast Wnut of ik
Cathedral of St. Paul's, London, before the fiie; >t
Stephen's, Vienna; Stnsburg, Cologne, the Towsr tf
Mechlin, and the Great Pyiamid of Eggrpt, to one a«k
folio print, it,
939. Flan of Westminater Hall and the w^iaccBt U»
Courta, Is.
933. View of the West Fh>nt of the PrapylaM at Athcw
folio. Is. dd.
934. M^ of Attica with part of Boeotia, improved fraa
the observations of recent traveilera, partieolarly bv Capcsu
Smith, R.N., 9s. 6rf.
935. Portraits of Eminent Ardiitects and Enaimcia, mez
who have done honour to Britsin. Engvwvod^ tfe ktst
style by superior artista, folio and 4to. ssaea, j^l. is. ckc
Set:
1. Sir Christopher Wren.
9k James Stuart.
8. Nicholas Revett.
4. Sir WiUiam Chamben.
5. James Watt.
6. Humphrey Repton.
7. Thomas TeUbnL
8. Thomas Tkedgold.
936. Transverse Section of the Temple of Jopitcr Otyn-
pius at Agrigentum, folio siae, is. (M.
937. Mr. Blair's Drawing of a Coriatfaial Chyltal, tiA^
grq>lied, large siie, 9t. dd.
938. Mr. Cheffln's large Uthographed Print of the Loa-
don and Birmingham Railway Entrance Fkont of 1^
London Station, 5s.
I
239.
Fine large print, At.
SHEER DRAUGHT OF HER MAJESTY'S STEAM SHIP OF
WAR ''MEDEA,''
Built by Oliver Lang, Esq. at Woolwich ; first commanded by Captain H. Au8tin in the MeditexniieiD
for nearly four years, and since on the North American station by Captain Nott.
I
ARCHITECTURAL LIBRARY^ 59^ HIGH HOLBORN,
29
PREPARING FOR PUBLICATION IN THE COURSE OF
THE YEAR 1840.
240.
THE PUBLIC WORKS OF THE UNITED STATES,
CONSTRUCTED BY EMINENT AMERICAN ARCHITECTS AND ENGINEERS;
Consisting of Plans, Elevations, and Sectional Details of all the principal Improvements of the States.
By WILLIAM STRICKLAND, Architect and Engineer,
EDWARD H. GILL, and HENRY R CAMPBELL, Engineers.
THB FOLLOVeiNG SUBJBCT8 ARJS PRBPARINO :
Plan, Elevation, and Sections of the Bank of the
United States, Philadelphia.
Plan, Sections, and Details of a Locomotive Steam
Engine, as constructed by M. W. Bald'win,
Philadelphia.
Plan, Elevation, and Section of the double outlet
Lock on the Schuylkill Canal at Plymouth,
Pennsylvania.
Plan, Elevation, and Sections of the Schuylkill
Viaduct on the Columbia and Philadelphia
Railroad, Pennsylvania.
Plan, Elevation, and Sections of a Timber Dam,
on the Sandy and Beaver Canal, Ohio.
Plan, Elevation, and Sections of the United States'
Mint, Philadelphia.
Plan, Elevation, and Sections of the Schuylkill
Permanent Bridge, Philadelphia.
Plan, Elevation, and Sections of the Philadelphia
Exchange.
Plan, Elevation, and Sections of the Philadelphia
Gas-works.
Plan, Elevation, and Sections of the Stone Via-
duct over the Schuylkill River at Fhoenizville,
Pennsylvania.
Plan, Elevation, and Details of a Locomotive
Steam Engine, as constructed by H. R Camp-
beU.
Plan, Elevation, and Section of the Philadelphia
County Prison.
Plan, Elevation, and Sections of a Cut Stone
Aqueduct, constructed over the James River,
Virginia, on the James River and Kanawha
Improvement.
Plan, Elevation, and Section of a Canal Bridge.
Plan, Elevation, and Sections of the Philadelphia
Alms-house.
Plan, Elevation, and Sections of the Ginrd Col-
lege for Orphans, Philadelphia.
Plan, Elevation, and Sections of the Fairmount
Bridge, Philadelphia.
Plan, Elevation, and Sections of the Philadelphia
Water-works, with a Map of its location.
Flan, Elevation, and Details of an improved Eight-
wheeled Day and Night Passenger Car, aa
used on many of the Railroads in the United
States.
Plan, Elevation, and Sections of the United States'
Naval Asylum, near Philadelphia.
Plan of the Aqueduct over the Allegheny River, at
Pittsburg, Pemisylvania.
Plan, Elevation, and Sections of a Canal Lock,
with improved gates, Sandy and Beaver Canal,
Ohio.
Plan, Elevation, and Sections of the Exchange
Buildings at New York.
Plan, Elevation, and Sections of the Eastern Peni-
tentiary at Philadelphia.
Plan of the Reservoir Mound and Gates, with
Details, on the Schuylkill Canal, near Pottsville,
Pennsylvania.
Plan, Elevation, and Sections of a Cut Stone Aque-
duct being constructed on the line of the New
York Water-works.
Plan, Elevation, and Details of the Troy and Sara-
toga Viaduct and Draw constructed over the
Hudson River, New York.
Plan, Elevation, and Sections of the Bridge over
the Delavrare River at Trenton, New Jersey.
Plan, Elevation, and Sections of a Stone and
Timber Lock, as constructed on the Schuylkill
Canal, Pennsylvania.
Plan and DetaUs of a Hudson River Steam Boat
for Passengers.
Plan and Details of the Delaware Breakwater at
the entrance into the Bay of Delaware.
Plan of the Timber Dam constructed across the
Swatara Union Canal, Pennsylvania.
Plan, Elevation, and Section of the Stone '^aduct
at the " Horse Shoe Bend," Allegheny Portage
Railroad, Pennsylvania.
Plan of a Burden Car with Eight Wheeh, as used
on the Pennsylvania Railroad.
Plan, Elevation, and Sections of the Towing Path
Bridge, constructed over the Schuylkill lUver at
Manayunk, Pennsylvania.
Plan, Elevation, and Sections of a Steam-boat
Lock, as constructed on the Kentucky River,
Kentucky.
Plan and Details of a Floating Dry Dock, now in
use on the Mississippi River.
Plan, Elevation, and Sections of a Timber Bridge,
as constructed by Col. S. H. Long.
®~
30
PREPARING FOR PUBLICATION BY JOHN WEALE^
Sections and Details of the various Rails used in
the United States.
Plan, Elevation, and Sections of a Cut Stone
Aqueduct, constructed on the Chesapeake and
Ohio Canal.
Plan of a Lock of 30 feet lift, oonsimctcd on O.
Lehigh Canal, Pennsylvania.
The Plates will be engraved by Mr. John Le Keux in his best style, and to be sold in the sepuvt
Divisions of A, Architecture,
B, Mechanical Engineeiing,
C, Civil Engineering.
To be published on fine Imperial folio paper, in Parts of 20 Plates, faced by a particular I>escn{6^
of the Subject. Price £1, in England, and 5 dollars in the States.
241.
THE PUBLIC WORKS OF GREAT BRITAIN,
VOL. II.
To be published in Parts of 20 Plates, engraved by Mr. John Lb Kkux and the best EngniTers; et
Plate to be faced by a particular Description of the Subject. Price £1. each Part.
The following are some of the very important subjects chosen from the highly scientific iroria
George Leather, Esq., C.E., of Leeds.
Cast Iron Aqueduct over tke Biver Calder at Stanley
Ferry, near Wakefield.
Ooole Docks and Locks.
Goole Lock Gates, with the machinery for opening and
shutting thcui.
Goole Bascule or Hoist Bridge.
Hull HoUt Brid((C.
Aire and Calder Navigation.
— Goole Canal.
Biver Don Navigation.
General Flan of Aire and Calder Navigation, from
Leeds and Wakefield to its junction with the Goole
C^mal at Ferrybridge.
Do. do. from. Ferrybridge to Ooole, with
the Docks at the latter place.
General Transverse Section of the Canals, with the
aide walls, &c.
Two examples of Locks,>-a Flood Lock and a Fall Lock.
Two Stone Bridges— one square, another askew.
One Swivel Bridge.
A Drainaee Culvert and a Warping Sloiee.
A set of Lock Gatea, both geosnMricaUy aad
trically projected.
Double acting Cloughs and Drawing Gccr. Ca^
and Anchors, Pivota and Steps, Forcbsty Dcfrcar
and other Iron-work coBD«eted with the
Lock and Bridge Keepers* Honaea.
Dunham Bridge,— Details, Elevations, &c.
Hunslet Bridge, Leeds.
Astley Bridge.
Honk Brid^, Leeds.
Victoria Bndge, Leeds.
Oott's Bridge, Leeds.
Thorp Hall or Waterloo Bridge, near Leeds.
Stockton and Hartlepool Railway.
Public Road Bridge under.
Occupation Brid^ under.
Do. do. (iron).
Sea Embankment at Straaton.
Nocton, &c. Drainages.
These will form 50 weU-occnpied Plates.
The following, in continuation, of other eminent Engineers, are also in preparation.
\
St. Kathcrinc's Docks — Form of Shoes used for Bay Piles
of Coffer-dam.
■ Form of Shoes used for Sheetinir
Piles.
— — — — Abutment for Swivel Bridge.
— — ■ Dock Gates.
Plans of Coffer-dam (2).
- — ■ Transverse Section of Coffer-dam.
Truss of the Roof over the Long Room, Custom House,
London.
Coal Jetty at Coffin's Wharf, Cardiff.
Taff Vale BaUway CulverU.
Pug Mill. Screw Jacks, Wliecl Barrows, Draw Crabs.
Tram Plates.
Weir for Bromley Mill.
Telford's Timber Turn Bridge on the Grand Surrey Canal.
Tewkesbury Severn Bridge.
Centering for Balloter Bridge across the River
Dee, Aberdeenshire.
Splendid Drawings of various Cranes.
Middlewich Branch of the Ellesmere and Chester Canal.
Cross Section of Culvert for conveying the Feeder under the
Glamorganshire Canal and Merthyr Road, and longitu-
dinal Section.
Pile Driving.
Bute Ship Canal— Travelling Crane.
— — — ^-^— Winch, Pmion Wheal, Barrel
Tilting Wivgons.
— — Inner Basin, Masonry
— ' ' Communication Locks.
—- Hollow Quoin of Entrance ^^
• Swivel Waggon— Stone Wmnait.
Counterforta, Sectiona.
■ Dock Gates, &c.
Foundry Cranes.
Plan and Section of the Great Sea l4>ek
Lowestoft.
&B.->
Port-Glas^w Wet Dock Lock Gate.
Swing Bndge between outer and -inner
Eastern Docks, Custom House, Loodon.
Outfall at the N. W. comer of Cardiff Caade.
Bridge at northern entrance to Cardiff Castle.
Bridge at N. W. corner of Cardiff Castle, aero^. w^^ - .
Bute Ship Canal. -«^»« re«..|
Newport Road Bridge across Feeder of Bute SKi^ c»r i
Crane at Harrison's Wharf, London, canahlfc r.f -*
five tons, cost jff 135. ' «« .-i
ARCHITECTURAL LIBRARY, 59, HIOH HOLBORN.
31
242.
In 8vo.y with Plates, a Second Edition of
A PRACTICAL TREATISE ON LOCOMOTIVE ENGINES
UPON RAILWAYS;
The construction, the mode of acting, and the effect of Engines in conveying heavy loads ; the means of
iscertaining, on a general inspection of the Machine, the velocity with which it will draw a given load,
ind the results it will produce under various circumstances and in different locaUties ; the proportions
v-hich ought to he adopted in the construction of an Engine, to make it answer any intended purpose ;
he quantity of fuel and water required, &c. ; vnth Practical Tahles, showing at once the results of the
'onnulae: founded upon a great mant new experiments made on a large scale, in a daily
tractice on the Liverpool and Manchester, and other Railways, with different Engines and Trains of
carriages. To which is added, an Appendix, showing the expense of conveying Goods by means of
A)comotive8 on Railroads.
By COMTE F. M. G. DE PAMBOUR.
243.
A New Edition, with Additions, by G. Rennib, Esq., C.E., F.R.S.
PRACTICAL ESSAYS ON MILL-WORK AND OTHER
MACHINERY.
n the Teeth of Wheels, the Shafts, Gudgeons, and Journals of Machines ; the Couplings and Bearings
' Shafts ; disengaging and re-engaging Machinery in Motion ; equalizing the Motions of Mills ;
langing the Velocity of Machines in Motion ; the Framing of Mill-Work, &c. ; with various useful
ibles
By ROBERT BUCHANAN, Engineer.
rnsedf with Notes and Additional Articles, containing new Researches on varioas Mechanical Subjects,
By THOMAS TREDGOLD, Civil Engineer.
Illustrated by Plates and numerous Figures. 2 vols. 8vo.
244.
4to., Price £1. la. Corrected and enlarged.
THE CARPENTER'S NEW GUIDE.
ing a complete Book of Lines for Carpentry and Joinery, treating fully on Practical Geometry,
ffits, Brick and Plaster Groins, Niches of every description. Skylights, Lines for Roofs and Domes ;
th a great variety of Designs for Roofs, Trussed Girders, Floors, Domes, Bridges, &c. Coppcr-
ites : including some Observations and Calculations on the Strength of Timber.
By P. NICHOLSON.
245.
Fourth Edition, improved and enlarged. 8vo., Price 12«. boards.
PRACTICAL ESSAY ON THE STRENGTH OF CAST IRON
AND OTHER METALS;
ended for the Assistance of Engineers, Iron-Masters, Millwrights, Architects, Founders, Smiths,
I others engaged in the Construction of Machines, Buildings, &c. Containing Practical Rules,
jles, and Examples, founded on a Series of new Experiments ; with an extensive Table of the
)p€rtie8 of Materials. Illustrated by Eight Plates and several Wood-cuts.
By THOMAS TREDGOLD, CivU Engineer.
* *
2 MR. WEALB'S supplementary LIST.
WMtem Europe, Mr. Wsalb htm for lome UnM pMt been engiced In the picpentloa, under eompaCflBt eaper-
intendenoe* off a large Oeou>oicAi« Map of
ENGLAND, WALES, SCOTLAND, IRELAND, FRANCE. GERMANY,
SWITZERLAND, AND PORTIONS OF ITALY,
AND OF THE AUSTRIAN AND PRUSSIAN STATES.
Without entering into an enumeimtkn of all the authorities which hare been ooneulted in the prepamtion of each
a Mao. it wUl beraffldent here to state that it b baaed upon the obserratlonc of the most eminent Britld» and
fofolni GeolofflsU, and includes in a digested form the most recent of their labours. The siie of the ICup Is as
inches bv 264inches, dimensions which unite to oonvenienoe for reference the practicability of a aeale sulBcicBtly
Urse to admit of the inseitlon of all the more important aeological and gcagraphical features of the ef-»*-«—
delineated. In order to render it as much as possible an exhibition of the Phmteal Gmgraphtf as well as the
of these oouutries, the names not only of the larger rivert, but also of their tributaries, as well as of smaller ai
have been inserted ; and particular attention haa been given to the ooneet Indieatkm of the numerous small srmms
and chains wliieh form parts of the mountain systems of Britain, France, Germanj, Switaerland. and Italy. The
etoratlon attained by the higlier summits of each of the principal diains is specified In English feeU K»hihHii^
thus the geofrraphical as welTas geological features of the countries represented, the Map to well calculated to Ibcm
a useful giiide In the oonsideraSon of the ▼arious lines of Rallraad whieh are either constructed or In piofiess
throughout Tarious parts of them.
The Map to handsomely engraved on steel, and the various geokialcal formations will be bcautifttny oolonnd fa
aeoordanoewith the system adopted in the most recent works of KngUih geologists of eminence.
In sheet, eoloured, 30*. Mounted on rollerB, £> Ss. In a ease for the library. £8 Sfc
251.
Papers on Iron and Steel, Practical and Experimental, with copioos iUastmtiYe
notes, by
Dayid Mushst, Esq.
Honorary Member of the Geological,' and the Qud>ee Literary and JlistoHeal
Societies; of the Institution of Civil Engineers of London; Corresponding
Men^rofihe WemerianNa,tural History Societyy Edinburgh. Lam and thick
royal Svo volume, with several plates^ in extra doth boards^ price 1/ 10«.
*• He has enriched hto native country with a discovery, which to Invaluable t he has suceeded by petknt and la-
borious Investigation in evolving the properties of minerato, the moat Important to our national prosperitys and be
has fixed the clearest principles of operation in all matters relating to the manufketure of iron and sted. It to dw
to any one who even oardessly reflects upon the subject, that the production of iron from the Aidon and eepaitfloo of
the parts in msMca of Iron-etone, cont^ning a fluctuating quantity of the ore sought to be extracted, must depeskl
upon a chemical agency, and therefore upon a knowledge of combinattdn and dfisolutlon, mhkh can alone be ae-
qulred by repeated experiments and by aecuracy of observation, and demands a knowledge of practical philoeophy,
only to DC attained by a development of its principles, in fkct, by a discovery through an of naturefs secrec i^
In the manufacture of iron, therefore, the materials used, the component puts of the iron-stone Itadf, their
upon the quality of cast-iron, the use of limestone as a deanser of earthy mixtures, an examination into thai
produced by flie nature, compiesslon, and velocity of the Mast ; the comparative merits of cokes and **>*y*e'. the*
very construction of the blastfurnace itself, these and a thousand other ramiflcatkms of the salijleet, mutt be the
legftimate and anxious themes for philosophical enquiry. Unless one should be wdl acquainted with the varied
ohaiaeter of the mineral relics contained in the bosom or the earth, the extent and benefit of Mr. Muahet^ labonn
can hardly be appreciated. To arrive at something like definite terms, definite principles, definite knowledge, and
definite oonduMons; In fact, to make metallurgy a science wu hto aim, and In that he has been triumphemly sve.
oessftal— end yet it to most extraordinary that of the many iron-masters, who are dally reaping the benefit of Us
researches, aoopting hto nomenclature, living upon hto suggestioos, and crowing rich oy hto expnienoe, there ate
scarcely three who have any extensive and thorough acquaintance with the science. Thenapers contained in the
magnificent volume before us, comprise the result of hto experiments fhnn time to time. The value of them to en-
hanced by the oopfous notes appenoed to them, comprising the rssults of later experience. For Inttanoe, we have aa
elaborate account of the application of heated air to the smelting of iron, andumesof Its efltets. Besidaa, there to
a moat Invaluable appendix, comprdiendlng an analysto of all the ooato found in the great coal dtotricts of »"g*—^
where the smelting and manufocture of iron prevtfto ; an analysto justly described oy Its author as * extensile,'
' laborious,' ' without parallel,* and we may add, of incalculable advantage to our national prosperity. To give aa
Idea of Uie fatigue endured upon some occasions, in hto experiments upon the shrinkage and expansion of cast Iran,
Mr. Mushet presents us with the following graphic account :— * From 1S8 deg. to IMd^. I felt a aenmttai of cold
similar to that when approaching a fire in winter, accompanied by a considerable degree of shivering. About IBO
deg. thto sensation wore off, ana I felt oompamtively comfortable. Perqiiration had became so violeot, as to oedM
through all parts of my watoieoat, breeches, and stodungs. The workmen who carried the metal perspired In sndi a
manner aa to wet their large aaeking trowaers aa if they had been aoa^d in-.water. The mobture tan In anch tor-
renta from their faces and anna aa to be dlatinctly heard hbsing upon the heated moulda. Their atep and aroM weie
now more agitated than I had ever before otaaerved. and the ainewa all over thrtr bodica were unoonSnonly lane and
felt inflateolto a great degreOi Two men performed the whole labour of pouring ; ro that each of them In 32 inmnln
carried half a ton of metal in quantltlea. In hand ladles, from S0 to <0 nounda eadi time. The apaee gone thiOMh
each time, the return with the empty ladle Included, was neariy ISO feet, or ftilly equal, upon the whole travel, to
half an English mile; the half of which space was traversed with a todle, metal Included, weighing 80 poun^ One
of the men immediately after thto operation, emptied- a pitdier of spring water at one draumt, whl^ I — ^i^tt^tit at
five English pints. At the 3rd cast the thermometer rose to 164 deg. When the cest was finished I had the doon and
windows shot. Thto made the real state of the moulds visible. The 18, 94, and S-pounders (cannon-ball) were aO
of a dtf k glowing red heat, and presented an arid and Inhospitable glare, with whidi It was Impoesible long to exist.*
(pp. 808, C) What will the Chaberu and other fire-kinga say to thto i Would the oven of the llluscriou^rsnclunan,
co-tenant with hto beef-steak, have produced by Ita cooking heat and eflbet graeter than the following, expettotteed
by the son of science ?—' One day a spirit of wine thermometer burst In my hand with a report like a pisiol :* p.
SOU We must mention the discovery of the Blackband, or Mushet'etone. alhided to above, as one InMance aaoM
many of the st^id advantages derived from Mr. Mushef s researehes to the country at large, and for which he hS
. tageai
earned that which will no doubt be dieerfully aoeordcd to him, tiie enthualaatie gratitude of the preeent ^
and of a posterity yet to comcb • The dtoeovery of thto stone was made In 1801, when I was engsged In ereettaMfov
myself ana partoers the Calder Iron Works. Chneat prejudice waa excited againat me by the tron<maalen and
ofuat day m preauminc to claaa the uriii coato of the country with iron-aton«s fit and proper for the btasMtamaee.
Yet that discoTery has cdevated Scotland to a consldemMe rank amongst the iron-making nations of Bnrope^ with
resources still In store that may be considered inexhauatlblek But such are the eoneolatory eflbeta of tfane net Che
<iiaooverer of 1801 to no longer oonaideted the intruaive visionary of the laboratory, but the acknowledged beneihelor
Ma country at large, and particularly of an extenalve daas of eoal and mine propitetuii and Iron maalrfi. who^svt
ItB. WBALB*S STTPPLBMEMTAHY LIST.
Dt illKDVcryi And who, ki thti^ilt of fnttaAil Kkoow-
• luoBumBital ncvd Dpan tbe not wbtn tb* dbciRBy
,T^jtt thiDUfllHHit the po*< of Uni Kdiime» In m nnlu
UU..V— ■ — - wworM. by ensourtg&a Ihaiouiuactiin sf Inn upon putoia-
Ilr.HiabMmnlmgttnioniliTTtlwCiiuhahuiMuInd, and to iMp.tb* buiot tf Ua bowBu Iw hat ddW«t-
uUf .imif-rf» riii»riiiwift*ii CArnUfi Sfpt. M. IMdL
d m Uill doMn* cnM naldi ftom Ihli
)u** pTODouDCMli mitt[*o(icra«aof|
lada. TPRtUa p. xtU.] Thu tbe liifiinu
td Item , will b> of onlUI wnlca (D th* '
252.
Papbbs on Subjects ' connected with the Duties op thk Corps of Royal Bm-
aiHEZBS, Vol. IV., 4U>, 30 ptatet, extra cfoM bound, U St.
CONTENTS.
Ntw Wilfh BrUn in Woolni^ Doek-Twd.
Single CoAeduntn Dltto-
-Wln)eellii( Cmml Into La] - ■ ■ —
Hi tbe EmplfmueDt of Send
TtaSii^
4 by the BulUiley Cora-
* lUUny Inn Br»d« onr lb*
u 5>-l>y, by tbe Bu&edey Ctn-
« lata Ciptmla DrommoDd, It.E., I
253.
Ornamental Ibon Wokk, Qatea, Lodges, Palisading, &c., of the Boyal Parks, in-
cluding the Plans of Regent's, Hyde, St. James's, and Qreen Parka, with the
Entntnces to the Sultan's Palace at Constantinople, 50 pUuet, in^erial 4to,
with a letter-press description of the recent ImproTements in the Perks, and
the £ntrtu)ce into London, haif-bouitd in momxo, price 2l 8t,
.W,,!
TBI POLLOWINQ IB
mm* tD St. Juw^i Fuk.
m of Renni'i Park.
irbti ARta, Buckis^um Fakeei plu u
Lodge of diUo. plu
ide. Hyde ■>»■, e
indeleTUlDD-
10. Hyde Puk Lddge, noni ud it
11. HmnuM Sodety ReeelTlng Hoin
t, OneeeDOT Lodge, front md
3. SUnbovfl Lodge, fie-' — ''
X. Lunp ud ItiUina, Chelien HonlUL
aPuti of Inn Wok ditto, to • iHHr iMta.
OMf, lUmpMBCaun, ISli C. Wnn.)
36. Dltta, ditto, dHIo,
M. Put! of lioB Woih, ditto, dlua
<l. Inn Work dfKtnu'iStelRM.dltta.
ti, PUn ud El*ntiOB of EMnsii* Lodax a&d Ii
Oetee at Onenwleb, (Sir C Wien.)
U. IHttD, dliia.laifcriMla.
4L Inn Oatei at OoDDanbury Pavk.
td. Plu.ElwrMkn.aadDelaiUofdJtta.
n. old BucUntflani Palaa EntTiiu, Inn OMee
17S7.
48. Lamp, Stirlb« CiMla.
■ide elermtUnu and plan.
tt Lodge, elrvaUon end ptau.
I& Hanorer Lodn. alevatlon aod plan,
17. Lamp at Hyde Paik Corner, with ihe detail*.
la Galea centre o/ Cdonnade. HydaPaik.
la IMailiafdIIto, quartet Mil iit.
so. nallincaltbehead of On BerpoiDne Rlier, Dmf
Oatea to Royal EntiaDca, DwaifRalUnf to Lodge,
n. Sun£opa Gate Ralli, Hyde fttk.
sa Cunbetland OWa Ralli, Hyde Paik.
ti. Paila and Detalta of pReedlnc.
W. RaUlai, Puk Squaie, RopsFi Patk.
With two beautiful »ood-eutt by Mr. Smith, of the past and present En-
trances at Hyde Park Corner, suggested for insertion, and the Drawings
contributed by Decimos Burton, Esq., Architect, to whom Mr, Weale is much
indebted for other contribnttons.
254.
Appendix A. and B. to TREDOOLn on Steak Navioaiiq„ ^tlas folio, with descriiptiTe
letter-press to both in 4to. The plates, 22 in Q.^.-.'bet) eibiW verj e\a>»iaie
d Timber Boats with the tT^ifli Unsoc, ■price ll 12*.
subjects of Iron and Timber Boats with the »
Appendix B. separate, for those who have b<t^J
4 MR. WBALB^S SUPPLEMBNTABY LIST.
255.
DOMESTIC ARCHITECTURE.
A SBRnts, with a particular deseription, of rery tagteftil examples of Interiots and
Exteriors of the Residences, of the Gentry erected in HambuiKh and its net^-
bourhood, principally in the Italian style, with Ornamental Pleasure Groimdsy
Verandas, Detached Cottages, &c., 19 fine jpiateM by A. de Chateaoneaf, in
large 4to, extra do^ boardi^ priee 1/ 1«. ; in large folio, with proof jdaies,
\l \U ed.
256.
LoKDON and Staines Bbidobs, magnificently drawn in Elevations and Plana, by
B. Albano, Esq., C.E^ and engraved in the finest style of art by Lowiy and
Le Keux, large size. London, 1 8«.— Staines, 12«.
257.
A Catalooub of Books on the subjects of Abghitbctubb ; Enoikbbbino, Civil,
MiLiTABY and Mbchanical; Naval Arghitigturb, and the Arts and
Manufactubbs of the Country ; classed, with an Index, by John Weale,
in 8vo, price 2« 6d.
258.
The Travellers' Club Housb, designed and executed by Charles Bany, Esq.,
Architect, with an Essay on the present state of Architectural Study and the
reyiTal of the Italian Style in Great Britain, by W. H. Leeds ; very fine plates
by Le Keux, consisting of Plans, Elevations, and Details, large 4to, kalf-
bound in moroocOy price 18«.
*< This is the oommeooenient of a publkfttloii ealculated to viadieite the duneter of EngUah ai^ilteets. aiid to
adT«noe the Mienoe of architecture itwIH * One material diflbrenoe, aa7> the preboe* ' between it and Merlous
woriu of the Jdnd whldi have been brought out in this eountry. whether as eoHections of buildfai^ br iJifliiin m
ardiitects, or the designs of an individual, is the completeness with whldi the buUdlnc selected for the vurpoee it
illustrated and elucidated, not only with rtgard to sections, as well as plans and elev^ioas, but also by oetaus and
parts at large \ without which latter the ot&r drawings lose much of their value, perhaps are in some ili^pM rather
Injurious to the youthftil student, because only the goleral fonns are presented to him i the oonseiiueniae of whkh
is that sufficient attention is not paid by him to that kind of character, and to that finish, wlildi depend imoo
detaiL'
*< Mr. Leeds begins his ' Essay on Modem English Architecture* by adverting to 'the peenliar, not to say
equivocal, position of archlteetun, occasioned by its compound character of a medianiosi and a tee art/ and to
the disadvantages to which it has been sutiject in oonsequenee. He proceeds to observe that, * looking at what has
been done within the last twenty or flve^ind-twenty yeers, although among the buildings erected within that peitod
we meet with many of considerable merit, we also ehoounter not a few that are quite the reverse eeitainly, very
far Inferior to what they might have bcw rendered by more diligent study and more artistlike treatinenL' He une^
as a stimulus to exertion on tlie subject, that * it should be borne In mind that the eyes of fore^picrs are upon h,
who, while they contemplate with astonishment of one kind our worlu of utility, our bridges, eaaals, tunnels,
raihroads, and constructions of that class, generally 'egerd with astonishment of a very different kind those of our
buildings in whidi, if any where, grandeur and reflnedtaste mi|dit be expected to display thcmselvt
'r,es the French express it, of the IHill" '
** The general idea, or motif, ts the Frendi express it, of the nil Mall Ront, appears to be derived ftom that of the
Palaiso Pandolflnl at Fknenoe, the design of which Is attributed to Raphael. Instead, however, of at all a— ,.j.^^.gf
from the origiiuUity of the English bmlding, the reeemblance that may be traced between the two servea only to
shew how mudi the beadties of a model may be improved upon by a frae imitation of it in the hands of a niMler.
There Is a siwKesse In the English palaaeo, which the Italian one does not possess, and more variety In lis Indlvidnal
Dsatures t it has also more unity m diaracter. It Is free from that heaviness in its general proportions, and fkom
dryness of style in the details, which merit Its archetype; and It further derives no small degree of addlttanal
elegance from the temodlke screen to the area, which converts into a podtive beauty— a graocftil, as well as a
pietureeque accompaniment— what Is almost taivariably alk>wed to be more or less a blemish. While it aeadsds so
perfectly with the other in Ita taste, that it would be ImposdUe not to recognise it Immediately as the productiaB ot
the same mind, even were It not known that the two elevations bdong to the same building, the garden fje^ade »^»m«
the iinpress of greater originality. The piquant dtteX produced by groupiiig together the three centre wlndowi of
each floor is as happy as it is unusual : this eompodtfon has an indeflnabfe charm, an attractive mm le dhe of
sentiment. Infinitely more captivating than that mere pomp of aidiitecture, which is frequently to be met with la
dtesigns thist, nevertheless, betray complete Inanity of ideas. Those who may be so disposed are at Ubeity to ssy
that there is not iqudi in it, after all— merely a few windows and rustics, and some other members of detail; la
short, nothing m<ffe than what any one else might have done. Very truei but, then, how are we to dlnwee of the
untoward question. Why have they not done so r Why should they— those, at least, who have practised the Italiaa
style— have forborne to avail themselves of it to the extent we now perodve it was posdble for them to have done,
had they been capable of bringing to It that geniality of feeling and taste, without which a work of aidiltcetufe
can never bea work of art, except of art at second-Jiand ; whatever it may be as a production of manual labour and
mechanical skill ? « • • e
« One quality in which this building to pre-eminent, and at present stands almost alone. Is the perfoct JbsM
(«
bestowed on every part. There Is not a dngie member, let Its situation be what it may, wliidi is not nibet earefuOy
studied and workra up, as will be evident on examining the plates of details i and, unices they are carefully ieeked
at, the merit of the elevations, particularly of that of the nrden front, cannot be ftilly appreciated in all tMr
piuticulars. TKls quality of teish can haraly be too strongly insisted upon, because It li precisely the very cne of
whidi we are apt to be careless. Hence the almost inexcusable inequalities which offiBOd the eye in eo many
structures otherwise not devoid of merit : paltry and misplaced economy In one put Is suflbrsd to Interfere with the
embellishment bestowed on others, and which is thereby sometimes rendered little better than tnmpcry and
misplaced ostentation. No doubt, some parts of a compodtlon, particularly where the dcdgn ie of
-'-- ^ " -.^^. OTy different thing ftom ^ '"
tent, ought to be treated as subordinate to others t but that to a very different thing ftnsb ncgtactiiig i«»., «•<»»«
last serves only to render them all the more conspicuous and obtrusive aa blemishes and seaie la the dasin,
las carefUl finish would have brought them foto proper keeinng with the net*
hB plates are beautifully execute^**— Liisrary Oeceffe.
» *
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